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In this article, I shed light on the role of digital media and friendships in migrants' inclusion and exclusion. Connecting the empirical findings of a qualitative, non-media centric, multi-method study to existing research in digital migration studies, digital media and friendship as well as the literature on inclusion and exclusion, I propose the concept of entangled inclusion and exclusion. This perspective underlines migrants' continuous (re-) negotiations of their situatedness in the (trans-)local spaces of the places they come from, move to and through. While playing diverse roles in migrants' development and maintenance of (trans-) local friendships, digital media contribute to non-linearities in migrants' subjective feelings of being included or excluded, making the processes involved more complex while also serving as material and symbolic signifiers of entangled inclusion and exclusion. [ABSTRACT FROM AUTHOR]

The status of any arrival city is far from stable, being continuously reworked by state policy, geopolitics, economic fluctuations or localised events that rupture or destabilise what came before. The diversifications and differential inclusions that are examined in this special issue attest to the complexities of arrival cities, where the very nature of 'arrival' is open to interpretation and subject to diverse temporal experiences and migration regimes. By approaching the concept of 'arrival city' as a heuristic and moving between the literal and figurative realms of mobility, I draw out some of the core contributions of Migrant-led Diversification and Differential Inclusion in Arrival Cities Across Asia-Pacific. This includes: the notion of arrival; temporal geographies and the experience of transience and non-linearity; and the geographies of intimacy and encounter. [ABSTRACT FROM AUTHOR]

The closely related processes of migration and diversification call for greater scrutiny of how contemporary arrival cities incorporate increasingly diverse groups of newcomers through practices and processes of differential inclusion. This special issue highlights arrival cities in the Asia-Pacific region, attending to how they are being transformed by the wide-ranging temporal and spatial dimensions of migrant-driven diversification. Rather than begin with how coexistence in the context of diversification ought to be, the collection of papers included here builds inter-references through contexts that are, ultimately, non-universal. In so doing, this special issue responds to recent calls by social scientists to extend our frames of reference beyond the dominant centres of knowledge production in Europe and North America in understanding the links between migration and urban diversity. The papers included here focus on arrival cities and urban places in Hong Kong, the Philippines, Singapore, Malaysia, Japan, Australia and New Zealand as an exercise in open-ended imagination, advancing the conversation on urban diversification in the age of global migration. We organise these forms of urban change and migration-driven differentiation along four key themes of temporalities, spatialities, intermediaries and norms that emerged from the collection of papers. Using these four conceptual themes, modes of differential inclusion function as tools of discipline and governance at one level, and are mobilised to subvert and negotiate power relations at another. As refracted through these four axes of analysis, differential inclusion draws our attention to the multiscalar and multi-actor politics of diversification. [ABSTRACT FROM AUTHOR]

Arrival cities are defined through migration-led diversification that structures integration, notably through everyday language practices. In Singapore's multilingual landscape, we find hints of historical waves of migrants from Southern China speaking Cantonese, Hakka, Hokkien and Teochew and the recent contributions of new migrants from Mainland China. In light of the work of Pennycook and Otsuji, this article explores how the norms of metrolingual multitasking – of adaptation through language – structure differential inclusion in Singapore through banal and commonplace interactions in shared spaces, such as markets. By focusing on historically situated linguistic scripts of inclusion and exclusion in the city-state, we contrast the linguistic adaptations of older and newer arrivals to show how integration is continuously constituted through the differential inclusion of new arrivals. Based on a series of interviews, we shed light on how metrolingual multitasking, as praxis of differential inclusion, sets up the normative framework for the coexistence of various linguistic forms and resources, whether recognised officially or not, and their use in creative ways for pragmatic communication in completing daily tasks. In this context, the norms of metrolingual multitasking reveal an overall sense of ordinary coexistence in living with such diversity as a requirement for successful integration, despite necessary instances of differential treatment and exclusionary practices, including a refusal to engage with difference. [ABSTRACT FROM AUTHOR]

This paper investigates consensus control problem for a class of distributed parameter type multi-agent differential inclusion systems with state time-delay by utilizing iterative learning control (ILC). Unlike most ILC literature of nonlinear distributed parameter systems that require an identical virtual leader, the virtual leader is iteratively varying in this work and can be described by any follower agent. Both P -type closed-loop and D -type open-loop ILC are proposed for the distributed parameter type multi-agent differential inclusion systems, which enable the output trajectories of each agent to achieve consensus in the sense of W 1 , 2 norm as the iteration number increases. Meanwhile, consensus control theorems for these protocols are established by using Steiner-type selector, Green's formulas and some technical inequalities. Finally, numerical simulations testify the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to analyze a sufficient condition ensuring the finite-time attractivity for the solutions to semilinear functional differential inclusions in Banach spaces. The obtained results will be applied to a class of partial differential equations. [ABSTRACT FROM AUTHOR]

This article challenges the claim that highly skilled international academics who have obtained advanced degrees and transnational identities are offered almost seamless mobility. The state border or territory is not the only line that highly skilled academics must cross as international subjects of mobility. Their high academic status is reduced to a precariat and confronted with epistemic injustices due to their immigration status. These include, but are not limited to, the waiting and processing times associated with immigration rules and visa requirements, which could also temporarily suspend mobility rights. The notion of a temporal border is enacted to explore the "time-bound" realities that highly skilled academics face. Border crossing for highly skilled migrants is not just a matter of entry passing through territorial lines of nation-states. The border has a "thickness" that stretches through time. Simply put, it takes time to cross borders. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of the following optimal solution for the system of differential inclusiony′ ∈ Φ(t,y(t)) a.e. t ∈ I = [t0,b] and y(t0) = u2,y′ ∈ Ψ(t,y(t)) a.e. t ∈ I = [t0,b] and y(t0) = u1.in a Hilbert space, where Φ and Ψ are multivalued maps. Our existence result is obtained via selection technique and the best proximity point methods reducing the problem to a differential inclusion.

In this paper we study an abstract system which consists of a hyperbolic hemivariational inequality coupled with a differential evolution inclusion involving a history-dependent operator in Banach spaces. A hybrid iterative system corresponding to the hemivariational inequality is introduced. Combining the Rothe method, a feedback iterative technique, and a surjectivity result for pseudomonotone operators, we establish existence and a priori estimate for solutions to an approximate problem. Next, through a limiting procedure for solutions of the hybrid iterative system, we show the existence of a mild solution to the original problem. Finally, we apply the main results to a dynamic contact problem in thermoviscoelasticity. [ABSTRACT FROM AUTHOR]

We study the constitutive set K arising from a 2 × 2 system of conservation laws in one space dimension, endowed with one entropy and entropy-flux pair. The convexity properties of the set K relate to the well-posedness of the underlying system and the ability to construct solutions via convex integration. Relating to the convexity of K , in the particular case of the p -system, Lorent and Peng (2020) [21] show that K does not contain T 4 configurations. Recently, Johansson and Tione (2024) [14] showed that K does not contain T 5 configurations. In this paper, we provide a substantial generalization of Lorent-Peng, based on a careful analysis of the shock curves for a large class of 2 × 2 systems. We provide several sets of hypotheses on general systems which can be used to rule out the existence of T 4 configurations in the constitutive set K. In particular, our results show the nonexistence of T 4 configurations for every well-known 2 × 2 hyperbolic system of conservation laws for which both families of shocks verify the Liu entropy condition. [ABSTRACT FROM AUTHOR]

Two classes of fractional integro-differential inclusions with certain boundary conditions are studied. The existence of solutions is established in the case when the set-valued map has nonconvex values. [ABSTRACT FROM AUTHOR]

The present paper proposes, in a real separable Hilbert space, to analyze the existence of solutions for a class of perturbed second-order state-dependent maximal monotone operators with a finite delay. The dependence of the operators is -in some sense- absolutely continuous (or bounded continuous) variation in time, and Lipschitz continuous in state. The approach to solve our problem is based on a discretization scheme. The uniqueness result is applied to optimal control. [ABSTRACT FROM AUTHOR]

There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability of a state-dependent integro-differential inclusion. The existence and uniqueness of solutions to a state-dependent functional integro-differential inclusion with delay nonlocal condition is studied. We, moreover, conclude the existence of solutions to the problem with the integral condition and the infinite-point boundary one. Some properties of the solutions are given. Finally, two examples illustrating the main result are presented. [ABSTRACT FROM AUTHOR]

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided. [ABSTRACT FROM AUTHOR]

We use some recent developments in Dynamics Programming Method to obtain a rigorous solution of the epidemic model formulated in [19] as an unsolved problem. In fact, this problem is proposed in the context of using Pontryagin’s Maximum Principle. We use a certain refinement of Cauchy’s Method of characteristics for stratified Hamilton-Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by a certain admissible control. The optimality is justified by using of one of the well-known verification theorems as an argument for sufficient optimality conditions. [ABSTRACT FROM AUTHOR]

Through this article, we aim to identify sufficient conditions to study the existence of solutions to a perturbed first-order iterative differential inclusion with maximal monotone operator. We provided examples to demonstrate our results. [ABSTRACT FROM AUTHOR]

Abstract This article investigates recently imposed restrictions in the asylum regimes in Denmark, Sweden and Norway. The purpose of the paper is twofold. First, we aim to identify general changes in asylum policies and asylum legislation. Second, we discuss and compare the policy tools, practices and legislation that have undermined the rights of unaccompanied Afghan minors. We also observe new tools of internal and external deterrence and restrictive asylum policies, combined with tighter border controls. In the case of adult asylum seekers from Afghanistan, high rejection rates and deportations were used for years as an important tool of deterrence. However, these tools were seldom used against unaccompanied Afghan minors before the large influx of asylum seekers in 2015. Since 2015, increased use of rejections, combined with temporary protections, have emerged as the major tools for restriction. We identify similarities and differences in the policy restrictions targeting unaccompanied minors between the countries. Although we identify some recent diverging trends in Scandinavian asylum policies regarding unaccompanied minors from Afghanistan, the general trend of policy restrictions still prevails in all three countries.

Abstract This article focuses on the labour market integration of highly qualified female refugees in cosmopolitan Berlin and smaller towns in the county of Brandenburg. Based on interviews with civil society organisations designed mainly for female refugees, universities, employees of the job agency and government administrations, the gendered pathways of stratified access of this group to the labour markets of the two areas were analysed. Special attention was given to the role of emerging intermediary actors and their powers to influence stratified access to the labour markets. As this research shows, a variety of new approaches have evolved, and a web of migration-related jobs to support these women has been created – with marked regional differences.

In this article, we give a new proof of the existence of absolutely continuous solutions for a class of first-order state-dependent maximal monotone differential inclusions. The existence result is obtained by using Schauder's fixed point theorem. In addition, a stability result is provided. Finally, using a suitable reduction of order technique, we give a new existence result for a general second-order state-dependent maximal monotone differential inclusion. [ABSTRACT FROM AUTHOR]

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints. A linear differential inclusion approach is implemented to formulate the saturation nonlinearity. Subsequently, a gain-scheduled dynamic output-feedback controller is structured to conform to the saturation representation. By means of a Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived for the analysis and feedback control synthesis of the closed-loop system in the presence of uncertainties and exogenous disturbances. Disturbance rejection objectives following an induced L 2 -norm and an L 2 − L ∞ norm formulation are examined. Estimation of the domain of attraction with the parametrisation of the admissible LPV controllers is presented. Three different optimisation objectives with respect to disturbance rejection, disturbance tolerance, and domain of attraction expansion are formulated. The proposed design methodology is examined in the context of the air-fuel ratio (AFR) regulation in a spark ignition (SI) engine with a speed-dependent delay and model parameters in the presence of canister purge disturbances and AFR dynamics uncertainty. The injector is restricted in the amount of fuel it can deliver to the cylinder. The three-way catalytic converter's performance in terms of oxygen storage and emission reduction is taken into consideration. Closed-loop simulation results are provided to validate the methodology. [ABSTRACT FROM AUTHOR]

We prove two existence results for functional differential inclusions governed by sweeping process. We consider the class of subsmooth moving sets. The perturbations depend on all the variables and their values are nonconvex. [ABSTRACT FROM AUTHOR]

The paper deals with second-order evolution problems driven by time and state dependent maximal monotone operators with non-Lipschitz perturbations. Systems governed by a couple of an evolution inclusion involving time and state dependent maximal monotone operator and a differential equation with fractional derivatives are also investigated. [ABSTRACT FROM AUTHOR]

In a Hilbert space H , we introduce a new class of first-order algorithms which naturally occur as discrete temporal versions of an inertial differential inclusion jointly involving viscous friction and dry friction. The function f : H → R to be minimized is supposed to be differentiable (not necessarily convex), and enters the algorithm via its gradient. The dry friction damping function ϕ : H → R + is convex with a sharp minimum at the origin, (typically ϕ (x) = r ‖ x ‖ with r > 0 ). It enters the algorithm via its proximal mapping, which acts as a soft threshold operator on the velocities. As a result, we obtain a new class of splitting algorithms involving separately the proximal and gradient steps. The sequence of iterates has a finite length, and therefore strongly converges towards an approximate critical point x ∞ of f (typically ‖ ∇ f (x ∞) ‖ ≤ r ). Under a geometric property satisfied by the limit point x ∞ , we obtain geometric and finite rates of convergence. The convergence results tolerate the presence of errors, under the sole assumption of their asymptotic convergence towards zero. By replacing the function f by its Moreau envelope, we extend the results to the case of nonsmooth convex functions. In this case, the algorithm involves the proximal operators of f and ϕ separately. Several variants of this algorithm are considered, including the case of the Nesterov accelerated gradient method. We then consider the extension in the case of additive composite optimization, thus leading to new splitting methods. Numerical experiments are given for Lasso-type problems. The performance profiles, as a comparison tool, demonstrate the efficiency of the Nesterov accelerated method with asymptotic vanishing damping combined with dry friction. [ABSTRACT FROM AUTHOR]

The present paper deals with the theory of duality for the Mayer problem given by second-order polyhedral discrete and differential inclusions. First, we formulate the conditions of optimality in the form of Euler–Lagrange type inclusions and transversality conditions for the polyhedral problems with second-order discrete and differential inclusions. Second, we establish dual problems for discrete and differential inclusions based on the infimal convolution concept of convex functions and prove the results of duality. For both primary and dual problems, the Euler–Lagrange type inclusions are "duality relations" and that the dual problem for discrete-approximate problems bridges the gap between the dual problems of discrete and continuous problems. As a result, the passage to the limit in the dual problem with discrete approximations plays a substantial role in the following investigations, without any which can hardly ever be established by any duality to the continuous problem. Furthermore, the numerical results also are provided. [ABSTRACT FROM AUTHOR]

A fractional differential inclusion defined by Caputo-Fabrizio fractional derivative with bilocal boundary conditions is studied. A nonlinear alternative of Leray-Schauder type, Bressan-Colombo selection theorem for lower semicontinuous set-valued maps with decomposable values and Covitz-Nadler set-valued contraction principle are employed in order to obtain the existence of solutions when the set-valued map that define the problem has convex or non convex values.

The mechanistic understanding of why neuronal population activity hovers on criticality remains unresolved despite the availability of experimental results. Without a coherent mathematical framework, the presence of power-law scaling is not straightforward to reconcile with findings implying epileptiform activity. Although multiple pictures have been proposed to relate the power-law scaling of avalanche statistics to phase transitions, the existence of a phase boundary in parameter space is until now an assumption. Herein, a framework based on differential inclusions, which departs from approaches constructed from differential equations, is shown to offer an adequate consolidation of evidences apparently connected to criticality and those linked to hyperexcitability. Through this framework, the phase boundary is elucidated in a parameter space spanned by variables representing levels of excitation and inhibition in a neuronal network. The interpretation of neuronal populations based on this approach offers insights on the role of pharmacological and endocrinal signaling in the homeostatic regulation of neuronal population activity.

In this paper, we approximate a nonautonomous neural network with infinite delay and a Heaviside signal function by neural networks with sigmoidal signal functions. We show that the solutions of the sigmoidal models converge to those of the Heaviside inclusion as the sigmoidal parameter vanishes. In addition, we prove the existence of pullback attractors in both cases, and the convergence of the attractors of the sigmoidal models to those of the Heaviside inclusion. [ABSTRACT FROM AUTHOR]

The mechanistic understanding of why neuronal population activity hovers on criticality remains unresolved despite the availability of experimental results. Without a coherent mathematical framework, the presence of power-law scaling is not straightforward to reconcile with findings implying epileptiform activity. Although multiple pictures have been proposed to relate the power-law scaling of avalanche statistics to phase transitions, the existence of a phase boundary in parameter space is until now an assumption. Herein, a framework based on differential inclusions, which departs from approaches constructed from differential equations, is shown to offer an adequate consolidation of evidences apparently connected to criticality and those linked to hyperexcitability. Through this framework, the phase boundary is elucidated in a parameter space spanned by variables representing levels of excitation and inhibition in a neuronal network. The interpretation of neuronal populations based on this approach offers insights on the role of pharmacological and endocrinal signaling in the homeostatic regulation of neuronal population activity. [ABSTRACT FROM AUTHOR]

To appease public anxieties and limit exploitation, in recent years Canada has sought to more strictly regulate and reduce temporary migrant work, while expanding opportunities for international mobility. This article explores the division between mobility and migration in this settler colonial context by charting developments in two overarching Canadian immigration program streams dedicated to facilitating international migration for employment on a temporary basis – the Temporary Foreign Worker Program (TFWP) and the International Mobility Program (IMP) – focusing on the latter. Through an analysis of underexplored IMP subprograms directed at 'national competitiveness,' it probes the extent to which several fast-growing IMP subprograms entail a departure from temporary migrant work under exploitative conditions. Questioning the validity of the migration/mobility distinction assumed in policy discourse, it argues that far from providing for ideal conditions for 'mobile' workers, Inter-Company Transfer, Postgraduation, and Spousal subprograms are characterised by conditions poised to heighten exploitation. Meanwhile, many participants in these subprograms migrate from source countries with a history of subordination through differential inclusion, illustrating how the application of migration control devices is bound-up with residues of formal barriers to entry forged on the basis of nationality and the institutionalised racism that they engendered and threaten to perpetuate. [ABSTRACT FROM AUTHOR]

Precarious legal status trajectories (PLSTs) are marked by periods without state authorisation and/or forms of temporary authorisation. They are temporally prolonged and directionally unpredictable, and may be spatially, juridically and substantively discontinuous. Their complexity poses challenges for researchers interested in the relationship between changes in legal status and differential inclusion. We examine the trajectories of illegalised Anglo-Caribbean and Latin American migrants living in Canada in the mid-2000s who applied for one or both of two humanitarian legal status adjustment mechanisms to obtain permanent residence: late refugee claims and applications on humanitarian and compassionate grounds. Despite sharing early illegalisation, we find regional racialised and gendered differences in their PLSTs. We present a framework for understanding how different trajectories are populated, and how the somewhat unpredictable outcomes of adjudications may lead to further applications and a reorganisation of PLSTs. We conceptualise PLSTs as assembled through (1) colonial legacies and histories of migration that contribute to racialised humanitarian deservingness, (2) state policies and humanitarian adjudication procedures, and (3) everyday encounters between migrants and other social and institutional actors. Our analysis shows how these elements come together and generate variable PLSTs and multi-dimensional differential inclusion. [ABSTRACT FROM AUTHOR]

The paper is devoted to Lagrange problem of optimal control theory with higher-order differential inclusions (HODI) and special boundary conditions. Optimality conditions are derived for HODIs, as well as for their discrete analogy. In this case, discretization method of the second-order differential inclusion is used to form sufficient optimality conditions for HODIs and periodic boundary conditions, the so-called transversality conditions. And to construct an Euler–Lagrange-type inclusion, a locally adjoint mapping is used, which is closely related to the coderivative concept of Mordukhovich. In turn, this approach requires several important equivalence results concerning LAMs to the discrete and discrete-approximate problems. The results obtained are demonstrated by the optimization of some "linear" optimal control problems, for which the Weierstrass–Pontryagin maximum principle and transversality conditions are formulated. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of abstract fractional differential inclusion with finite delay in which the multi-valued nonlinearity is possibly superlinear. We analyze some sufficient conditions that ensure the global solvability of problem. Our main result is the existence of a compact set of decay solutions to our problem by estimating the measure of noncompactness and using the fixed point theory for a condensing map. The obtained results will be applied to a concrete polytope fractional differential system. [ABSTRACT FROM AUTHOR]

Summary: In this article, we are concerned with fuzzy Clifford‐valued Cohen‐Grossberg neural networks (FCVCGNNs) via discontinuous activations and time‐varying delays. First, the time‐delayed feedback strategy is used to investigate the synchronization in finite‐time and fixed‐time of FCVCGNNs with discontinuous activations and time‐varying delays. By designing Lyapunov functions and utilizing differential inequalities, several effective conditions are derived to ensure synchronization in finite‐time and fixed‐time of the addressed neural networks. A novel fixed‐time convergence method is proposed to study synchronization in fixed‐time of discontinuous delayed FCVCGNNs. Furthermore, the settling time of synchronization are estimated. In the end, two numerical examples with simulations are given to confirm the effectiveness of the synchronization criteria. [ABSTRACT FROM AUTHOR]

This study focuses on the exploitation and control of Sub-Saharan migrants who pick tomatoes in the Capitanata area in the South Italian region of Puglia. Large-scale organised distribution puts pressure on the growers to seek cheap agricultural labour, which is currently largely provided by migrants. The historical phenomenon of the caporalato labour contracting system is still widely practised and impacts in particular the Sub-Saharan migrants. Through the application of the concept of differential inclusion, the study focuses on the subordinate layering processes to which the Sub-Saharan migrants are subjected: racialisation, 'refugeeisation', criminalisation, deportability and invisibility. The ethnographic case study of the 'taxi-driver' sheds light on the difficulty in identifying caporali who have traditionally been blamed for a system that exploits labourers while instead protecting the owners. Recent anti- caporalato laws have been ineffective in contributing to the creation of a more just labour system and have only served to increase the pressure on the Sub-Saharan migrants for whom work is synonymous with survival. • Historically, the caporalato labour contracting system recruited agricultural workers; today it exploits Sub-Saharan migrants. • Unsustainable prices dictated by the large-scale corporate distribution effectively increase worker exploitation. • The differential inclusion of migrant workers manifests itself through the processes of racialisationand criminalisation. • The police and media in Italy create negative narratives that portray migrants as criminals: sometimes this is overturned. [ABSTRACT FROM AUTHOR]

We study a free-time optimal control problem for a differential inclusion with mixed-type functional in which the integral term contains the characteristic function of a given open set of "undesirable" states of the system. The statement of this problem can be viewed as a weakening of the statement of the classical optimal control problem with state constraints. Using the approximation method, we obtain first-order necessary optimality conditions in the form of the refined Euler–Lagrange inclusion. We also present sufficient conditions for their nondegeneracy and pointwise nontriviality and give an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we propose a neural network modeled by a differential inclusion to solve a class of discontinuous and nonconvex sparse regression problems with general convex constraints, whose objective function is the sum of a convex but not necessarily differentiable loss function and L 0 regularization. We construct a smoothing relaxation function of L 0 regularization and propose a neural network to solve the considered problem. We prove that the solution of proposed neural network with any initial point satisfying linear equality constraints is global existent, bounded and reaches the feasible region in finite time and remains there thereafter. Moreover, the solution of proposed neural network is its slow solution and any accumulation point of it is a Clarke stationary point of the brought forward nonconvex smoothing approximation problem. In the box-constrained case, all accumulation points of the solution own a unified lower bound property and have a common support set. Except for a special case, any accumulation point of the solution is a local minimizer of the considered problem. In particular, the proposed neural network has a simple structure than most existing neural networks for solving the locally Lipschitz continuous but nonsmooth nonconvex problems. Finally, we give some numerical experiments to show the efficiency of proposed neural network. [ABSTRACT FROM AUTHOR]

In this paper, we prove a theorem concerning the existence and uniqueness of a solution for a degenerate sweeping process with a Lipschitz single valued perturbation in Hilbert space. An application to differential complementarity problems is given. [ABSTRACT FROM AUTHOR]

In this paper, we prove new compression–expansion type fixed point theorems in cones for the so-called decomposable maps, that is, compositions of two upper semicontinuous multivalued maps. As an application, we obtain existence and localization of positive solutions for a differential equation with ϕ -Laplacian and discontinuous nonlinearity subject to multi-point boundary conditions. As far as we are aware, the existence results are new even in the classical case of continuous nonlinearities. [ABSTRACT FROM AUTHOR]

The theory of differential inclusions has played a central role in many areas as biological systems, physical problems and population dynamics. The principle aim of our work is to compute explicitly the discrete approximate solution of a differential inclusion including a maximal monotone operator. Also we present a numerical application of our results for showing how to compute the discrete approximate solution of its corresponding differential inclusion.

Abstract This paper is devoted to study the existence of at least one continuous mild solution to semilinear fractional differential inclusion with deviated-advanced nonlocal conditions. We develop the results obtained, by exchanging the deviated-advanced nonlocal condition to an integral form. Our results will be accomplished by using the nonlinear Leray-Schauder’s alternative fixed point theorem. The main results are well illustrated with the aid of an example.

Existence of solutions for a Bagley-Torvik fractional integro-differential inclusion is investigated in the case when the values of the set-valued map are not convex.

In this paper, we consider the existence and uniqueness of solutions to the impulsive differential equations with inclusions involving Katugampola fractional derivative. With the help of properties of Katugampola fractional calculus and fixed point methods, we derive existence and uniqueness results. Finally, an example is given to illustrate our theoretical results.