Search

We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on fixed point index calculations for multivalued mappings and apply them to prove the existence of solutions to multivalued equations in ordered space, under flexible conditions for the positive eigenvalue.

The aim of this paper is to present a common fixed point theory for a pair of multivalued operators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to a nonlinear elliptic inclusion problem driven by an elliptic differential operator with Dirichlet boundary and a multivalued term depending on the solution and its gradient in reflexive Orlicz–Sobolev spaces by using a linear functional analysis method and a subsolution–supersolution method. We provide some sufficient conditions to ensure that a subsolution and a supersolution exist. An existence theorem for positive solutions of the problem is established. [ABSTRACT FROM AUTHOR]

A direct variational technique involving Clarke generalized gradient is used to treat general boundary value problems with discontinuous nonlinearities. Based on the theory of positive definite symmetric operators it is established the nonsmooth variational form of the regularized inclusions which give the Filippov solutions of the discontinuous problems. These solutions reduce to classical solutions in case that a transversality condition on the set of discontinuities is satisfied. The results apply to a wide class of concrete boundary value problems of different orders. Two illustrative examples are given. [ABSTRACT FROM AUTHOR]

We propose a time semi-discrete scheme for the Caginalp phase-field system with singular potentials and dynamic boundary conditions. The scheme is based on a time splitting which decouples the equations and on a convex splitting of the energy associated to the problem. The scheme is unconditionally uniquely solvable and the energy is nonincreasing if the time step is small enough. The discrete solution is shown to converge to the energy solution of the problem as the time step tends to 0. The proof involves a multivalued operator and a monotonicity argument. This approach allows us to compute numerically singular solutions to the problem. [ABSTRACT FROM AUTHOR]

Given a closed linear relation T between two Hilbert spaces H and K , the corresponding first and second coordinate projections P T and Q T are both linear contractions from T to H , and to K , respectively. In this paper we investigate the features of these graph contractions. We show among other things that P T P T ∗ = (I + T ∗ T) - 1 , and that Q T Q T ∗ = I - (I + T T ∗) - 1 . The ranges ran P T ∗ and ran Q T ∗ are proved to be closely related to the so called ‘regular part’ of T. The connection of the graph projections to Stone’s decomposition of a closed linear relation is also discussed. [ABSTRACT FROM AUTHOR]

By various examples we illustrate that the ordered set theory is far away from having unitary notations and terminology. Some suggestions for unifiying the terminology are also presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend Krasnoselskii’s fixed point theorem to the case of generalized Banach spaces for multivalued operators. As application, we will give an existence result for a system of Fredholm-Volterra type differential inclusions.

The aim of this paper is to present some best proximity results for multivalued cyclic operators satisfying a Ćirićtype condition. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we define the concept of weakly Reich-contractive operator and give a fixed point result for this type of operators. Then we study the data dependence for this new result.

The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators. As applications, we will give some existence results for abstract system of Fredholm-Volterra type differential equations and inclusions.

In this paper we present some fixed point results for multivalued operators, which extend the ones given by A.I. Perov and A.V. Kribenko, as well as some recent contributions due to A. Bucur, L. Guran and A. Petruşel.

Fuel moisture content (FMC) plays a significant role in wildfire behavior and rate of spread (ROS). In addition, FMC is a highly dynamic factor and very vulnerable to climate variations. Understanding the effect of FMC on the behavior of fire spread models is crucial, and detailed analysis of specific aspects of complex models is a very effective way to improve them. The simplified physical fire spread model PhyFire considers the effect of FMC in a novel way, involving a multivalued maximal monotone operator. Several numerical experiments have been carried out to confirm that the behavior of the ROS simulated with PhyFire involving FMC is as expected in the reviewed literature: an exponential decrease in fire ROS compared to FMC, for different scenarios, considering different fuel types, terrain slopes and wind speeds. PhyFire performs very accurately, proving that the multivalued operator used is suitable and consistent. • Fuel moisture content plays a significant role in wildfire behavior and its rate of spread, and it is one of the primary variables in many fire behavior prediction models. • PhyFire is a simplified two-dimensional one-phase physical fire spread model based on energy and mass conservation equations that models fuel moisture content through a multivalued operator. • The PhyFire model has been confirmed to be highly consistent with an exponential decay of fire ROS compared to FMC alone, and also in the presence of wind speed and terrain slope. [ABSTRACT FROM AUTHOR]

We consider a class of stationary subdifferential inclusions in a reflexive Banach space. We reformulate the problem in terms of a variational inequality with multivalued term and prove an existence result using the Kakutani-Fan-Glicksberg fixed point theorem. This approach allows to consider, in a natural way, a dual variational formulation of the problem. Next, we study the link between the primal and dual formulations and provide an equivalence result. Then, we consider a new mathematical model which describes the contact of an elastic body with a foundation. We apply the abstract formalism to derive the primal and the dual variational formulations of the problem, in terms of displacement and stress, respectively. Finally, we present existence and equivalence results in the study of this contact model. [ABSTRACT FROM AUTHOR]

We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces. [ABSTRACT FROM AUTHOR]

In this work we prove some extensions of the multivalued contraction principle and of Reich's fixed point theorem for multivalued operators in vector metric spaces. We also present a theory for the multivalued contraction principle in vector metric spaces in the spirit of the approach given by I. A. Rus and A. Petruşel. Some examples and open questions are pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we will present some fixed set and fixed point theorems for nonself multivalued generalized contractions. We will discuss the cases of multivalued contractions, multivalued φ-contractions and multivalued Kannan contractions. Our results propose some existence, uniqueness and related properties of the multivalued fractal generated by iterative multifunction systems. The approach is based on some new properties proved for the multi-fractal operator induced by a nonself multivalued generalized contraction. Some open problems are also formulated. [ABSTRACT FROM AUTHOR]

The purpose of this work is to present some generalizations of the well known Nadler's contraction principle. More precisely, using an axiomatic approach of the Pompeiu-Hausdorff metric we will study the properties of the fractal operator generated by a multi valued contraction. [ABSTRACT FROM AUTHOR]

Some fixed point theorems for a class of multivalued operators satisfying a generalized contractive conditions or multivalued Geraghty functions acting on a metric space endowed with a graph has been established. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of E-b-metric space and we present a singlevalued and multivalued nonlinear fixed point theorem in an E-b-metric space using the Picard and weak Picard operators technique. The proofs are based on the concept of strict positivity in a Riesz space introduced by Páles and Petre. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the existence and some qualitative properties of solutions of variational inequalities of the form: and of quasi-variational inequalities of the form: where is a second-order elliptic operator of Leray–Lions type, is a multivalued lower order term, and are convex functionals, and also depends on . We concentrate here in noncoercive cases and use sub-supersolution methods to study the existence and enclosure of solutions, and also the existence of extremal solutions between sub and supersolutions. [Copyright &y& Elsevier]

We present a multivalued nonlinear fixed point theorem in an E-metric space introducing the concept of strict positivity in a Riesz space. Our result extends some well-known fixed point theorems obtained by J. Matkowski, R. Wȩgrzyk, R. Cristescu, and C. Çevik, I. Altun. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present, as applications of some fixed point theorems, existence results for integral equations and inclusions.

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems are also presented. [ABSTRACT FROM AUTHOR]

Abstract: We are concerned in this paper with variational inequalities of the form: where is a maximal monotone operator, is an integral multivalued lower order term, and K is a closed, convex set in a Sobolev space of variable exponent. We study both coercive and noncoercive inequalities. In the noncoercive case, a sub-supersolution approach is followed to obtain the existence and some other qualitative properties of solutions between sub- and supersolutions. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss some new fixed point theorems for a pair of multivalued operators which satisfy weakly generalized contractive conditions. Our results are the extension and improvement of corresponding results of [J. Harjani and K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analysis, 71 (2009) 3403–3410] and [X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2007) 780–786]. Finally, some examples are given to illustrate the usability of our results. [Copyright &y& Elsevier]

Abstract: Recently, Bucur, Guran and Petrusel presented some results on fixed points of multivalued operators on generalized metric spaces which extended some old fixed point theorems to the multivalued case (Bucur et al., 2009 ). Also, Kikkawa and Suzuki have proved some results for generalized contractions in complete metric spaces (Kikkawa, 2008 ). In this paper, we shall give some results on fixed points of multivalued operators on generalized metric spaces by using the method of Kikkawa (2008) . [Copyright &y& Elsevier]

Abstract: In this paper,we discuss some new fixed point theorems for a pair of multivalued operators which satisfy generalized contractive condition. Our results are the extension and improvement of corresponding results of single-valued operators. Finally, some examples are given to illustrate the usability of our results. [Copyright &y& Elsevier]

The purpose of this paper is to study the data dependence for the fixed point set of a multivalued weakly contractive operator with respect to a w-distance in the sense of T. Suzuki and W. Takahashi. We also give a fixed point result for a multivalued weakly '-contraction on a metric space endowed with a w-distance. [ABSTRACT FROM AUTHOR]

The purpose of this work is to present some fixed point results for the so-called multivalued weak contractions. Our results are extensions of the theorems given by M. Berinde and V. Berinde in [1] and by C. Chifu and G. Petruşel in [2]. [ABSTRACT FROM AUTHOR]

We establish new results on the existence of positive solutions for a kind multi-point boundary value problem with multivalued operator. Our results are based on a recent Leggett-Williams theorem for coincidences of multivalued operators due to O’Regan and Zima. The most interesting point is the acquisition of positive solutions for the resonance case. And an example is constructed to show that our result here is valid. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16]. [ABSTRACT FROM AUTHOR]