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This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed.

In this article, by using the Schauder fixed point theorem, we first study the existence of solutions for a new coupled system of Caputo fractional differential equations with multipoint boundary value conditions under the assumption that the nonlinear term satisfies two types of the Carathéodory conditions. Using this result, we provide the existence of solutions of the system with infinite points and Riemann–Stieltjes integral boundary conditions, respectively, instead of doing it directly. Finally, we give three examples to illustrate the feasibility of main results.

Based on properties of Green’s function and by Avery–Peterson fixed point theorem, the existence of multiple positive solutions are obtained for singular p-Laplacian fractional differential equation with infinite-point boundary conditions, and an example is given to demonstrate the validity of our main results.

This paper investigates the abstract fractional stochastic evolution equations. A new existence result of the square-mean S-asymptotically periodic mild solutions are obtained under the assumption that the nonlinear terms only satisfy some growth conditions. Moreover, the uniqueness and asymptotic stability results of the square-mean S-asymptotically periodic solution are presented when the nonlinear functions satisfy the general Lipschitz condition. Finally, two examples are given to illustrate our main results. MR(2020) Subject Classification: 60H15; 47D06; 34G20; 46T20.

We begin by introducing some function spaces Lcp(R+),Xcp(J) made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces, next, we derive some new boundedness and continuity properties of Hadamard integral operators mapping on Xcp(J) and Xp(J). Based on this, we investigate a class of boundary value problems for Hadamard fractional differential equations with the integral boundary conditions and the disturbance parameters, and obtain uniqueness results for positive solutions to the boundary value problem under some weaker conditions.

In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dua...

In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. It is proved that for general initial data u 0 ∈ H s with s > 3 , the life span of the classical solutions satisfies T > C ln N 3 / 4 .

In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations are obtained via general Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and α-order solution operator.

In this work, the aim is to discuss a new class of singular nonlinear higher-order fractional boundary value problems involving multiple Riemann–Liouville fractional derivatives. The boundary conditions are constituted by Riemann–Stieltjes integral boundary conditions. The existence and multiplicity of positive solutions are derived via employing the Guo–Krasnosel’skii fixed point theorem. In addition, the main results are demonstrated by some examples to show their validity.

This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach.

In this paper, we study the mild solutions of a class of nonlinear fractional reaction–diffusion equations with delay and Caputo’s fractional derivatives. By the measure of noncompactness, the theory of resolvent operators, the fixed point theorem and the Banach contraction mapping principle, we develop various theorems for the existence and uniqueness of the global mild solutions for the problem.

In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and s...

By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is derived and some useful properties of the Green’s function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the positive solutions for the boundary value problem are established. Moreover, the unique positive solution that we obtained in this paper is dependent on $\lambda ,\mu $ , and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.

In this paper, we consider a new class of singular nonlinear higher order fractional boundary value problems supplemented with sum of Riemann–Stieltjes integral type and nonlocal infinite-point discrete type boundary conditions. The fractional derivative of different orders is involved in the nonlinear terms and boundary conditions, and the nonlinear terms are allowed to be singular in regard to not only time variable but also space variables. A unique positive solution is established by using the fixed point theorem of mixed monotone operator. In addition, some significant properties of the unique solution depending on the parameter λ are stated. In the end, two examples are worked out to illustrate our main results.

We investigate a class of semipositone fractional integral boundary value problem on the half-line. Using the fixed point index theorems in a cone, we obtain the existence result of positive solutions.

An input vector composed of various features plays an important role in short-term traffic forecasting. However, there is limited research on the optimal feature selection of an input vector for a certain forecasting task. To fill the gap, this paper proposes a cohesion-based heuristic feature selection method by analyzing the nature of the forecasting methods. This method is able to determine which features should be contained in an input vector to make a forecasting algorithm perform better. The proposed method is demonstrated in two experiments based on the empirical traffic flow data. The results show that the method is able to improve the performances of the short-term traffic forecasting algorithms. It is then suggested to consider the proposed method as a preprocessing procedure in practical forecasting applications.

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, nonlinear weak damping, and a superlinear source: $$ u_{tt}+\Delta ^{2} u- \int _{0}^{t} g(t-\tau )\Delta ^{2} u(\tau )\,\mathrm{d} \tau + \vert u_{t} \vert ^{m-2}u_{t}= \vert u \vert ^{p-2}u,\quad \text{in }\varOmega \times (0,T). $$ When the source is stronger than dissipations, we obtain the existence of certain weak solutions which blow up in finite time with initial energy $E(0)=R$ for any given $R\geq 0$ .

This paper discusses the abstract time-space fractional evolution equation with the Caputo derivative of order $$\alpha \in (0,1)$$ and fractional power operator $$-A^{\beta }$$ , $$\beta \in (0,1)$$ , where $$-A$$ generates a $$C_{0}$$ -semigroup on a Banach space. The compactness and exponential stability of the semigroup which is generated by fractional power operator $$-A^{\beta }$$ are investigated. With the aid of the properties of the semigroup, the existence and global asymptotic behavior of S-asymptotically periodic solutions are obtained by some fixed point theorems and related inequalities. An example to the time-space fractional diffusion equation with fractional Laplacian will be shown.

Low-carbon innovation can address both economic and environmental concerns; patterns of low-carbon innovation convergence can determine the effectiveness of mitigating the adverse consequences of climate change. Considering that economic openness has a huge impact on the development of innovation capability, this paper uses a conditional β convergence model to examine the convergence of low-carbon innovation in Chinese manufacturing industry and its relationship with economic openness. We incorporate the spatial spillover effect into the convergence function by constructing spatial error model, spatial lag model, and spatial Durbin model. Based on a panel data set of 30 Chinese provinces over the period 2004–2016, the results show that low-carbon innovation in Chinese manufacturing industry has a strong feature of conditional β convergence. The convergence rate of low-carbon innovation is slightly slowed down by economic openness, and the main reason is that the spillover effect is weak and the convergence rate is slow in lower open areas, so the convergence rate of the whole country is slowed down by that of the lower open areas. Although the economic openness in adjacent areas can contribute to the development of local innovation ability, but generally speaking, economic openness in local areas takes a stronger effect in promoting the convergence of low-carbon innovation than that in adjacent areas. The findings have important policy implications as they suggest the need for a more equal degree of economic openness among Chinese provinces to speed up the convergence of low-carbon innovation.

In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.

Background Minxian black fur (MBF) sheep are found in the northwestern parts of China. These sheep have developed several special traits. Skin color is a phenotype subject to strong natural selection and diverse skin colors are likely a consequence of differences in gene regulation. Methods Skin structure, color differences, and gene expression (determined by RNA sequencing) were evaluated the Minxian black fur and Small-tail Han sheep (n = 3 each group), which are both native Chinese sheep breeds. Results Small-tail Han sheep have a thicker skin and dermis than the Minxian black fur sheep (P P OCA2 melanosomal transmembrane protein (OCA2), dopachrome tautomerase (DCT), tyrosinase (TYR) and tyrosinase related protein (TYRP1), melanocortin 1 receptor (MC1R), and premelanosome protein (PMEL). The results from our histological and transcriptome analyses will form a foundation for additional investigation into the genetic basis and regulation of pigmentation in these sheep breeds.

A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows.

Objective. This study is aimed at comparing the image quality and diagnostic performance of mean apparent diffusion coefficient (ADC) and lesion-to-spinal cord signal intensity ratio (LSR) derived from turbo spin-echo diffusion-weighted imaging (TSE-DWI) and echo-planar imaging- (EPI-) DWI in patients with a solitary pulmonary lesion (SPL). Methods. 33 patients with SPL underwent chest imaging using EPI-DWI and TSE-DWI with b = 600 s/mm2 in free breathing. A comparison of the distortion ratio (DR), signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) was drawn between the two techniques using a Wilcoxon signed-rank test. The interprotocol reproducibility between quantitative parameters of EPI-DWI and TSE-DWI was evaluated using a Bland-Altman plot. ADCs and LSRs derived from EPI-DWI and TSE-DWI were calculated and compared between malignant and benign groups using the Mann–Whitney test. Results. TSE-DWI had similar SNR and CNR compared with EPI-DWI. DR was significantly lower on TSE-DWI than EPI-DWI. ADC and LSR showed slightly higher values with TSE-DWI, while the Bland-Altman analysis showed unacceptable limits of agreement between the two sequences. ADC and LSR of both DWI techniques differed significantly between lung cancer and benign lesions ( P < 0.05 ). The LSR(EPI-DWI) showed the highest area under the curve ( AUC = 0.818 ), followed by ADC(EPI-DWI) ( AUC = 0.789 ), ADC(TSE-DWI) ( AUC = 0.781 ), and LSR(TSE-DWI) ( AUC = 0.748 ), respectively. Among these parameters, the difference in diagnostic accuracy was not statistically significant. Conclusions. TSE-DWI provides significantly improved image quality in patients with SPL as compared with EPI-DWI. However, there was no difference in diagnostic efficacy between these two techniques, according to ADC and LSR.

In this paper, we present a new fixed point theorem for the sum of two mixed monotone operators of Meir–Keeler type on ordered Banach spaces through projective metric, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the scaling of the associated equations. In the functional setting as close as possible to the physical energy spaces, we prove the unique global solvability of strong solutions close to a stable equilibrium state. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we establish the time decay rates for the constructed global solutions. The proof relies on an application of Fourier analysis to a complicated parabolic-hyperbolic system, and on a refined time-weighted inequality.

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, a linear weak damping and superlinear source. Finite time blow-up results have been obtained for the case in which the initial energy $$E(0)\le M$$ , where M is a positive constant. By utilizing Levine’s classical concavity method, we give a new blow-up criterion which includes the case of $$E(0)>M$$ and derive an explicit upper bound for the blow-up time. By using the Fountain Theorem, we show that the problem with arbitrary positive initial energy always admits weak solutions blowing up in finite time.

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results.

In this paper, the isotonicity of the proximity operator and its applications are discussed. We first establish a few new conditions of the mappings such that their proximity operators are isotone with respect to orders induced different minihedral cones. Some properties and examples for these conditions are then introduced. We especially consider the isotonicity of the proximity operator with respect to one order induced by a subdual cone and two orders. To estimate the convergence rate of the iterative algorithms, some other inequality characterizations of the proximity operator with respect to the orders are then proved. As applications, some solvability and approximation theorems for the mixed variational inequality and optimization problems are established by order approaches, in which the mappings need not to be continuous and the solutions are optimal with respect to the orders. By using the isotonicity of the proximity operator with respect to two orders, we overcome the absence of the regularity of the order. The convergence rate of forward–backward algorithms is finally estimated by order approaches.

This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions under the hypothesis that the nonlinear term satisfies the Carathéodory conditions. We apply the Banach contraction mapping principle to obtain the uniqueness of solutions. Moreover, by using the theory of spectral radius we prove the uniqueness and nonexistence of positive solutions. Finally, we illustrate our main results by some examples.

In this paper, by using the cosine family theory, measure of non-compactness and the generalization of Darbo-fixed point theorem, we establish the existence of mild solutions of nonlinear second-order impulsive integro-differential evolution equations of Volterra type in Banach spaces. The result obtained herein generalizes and improves some known results.

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

Let $$G = (V(G),E(G))$$ be a graph and $$f:V(G) \to \{ 0,1,2\} $$ be a function where for every vertex $$v \in V(G)$$ with $$f(v) = 0,$$ there is a vertex $$u \in {N_G}(v),$$ where $$f(u) = 2.$$ Then $$f$$ is a Roman dominating function or a $$RDF$$ of $$G.$$ The weight of $$f$$ is $$f(V(G)) = \sum\nolimits_{v \in V(G)} f(v).$$ The minimum weight of all $$RDF$$ is called the Roman domination number of $$G,$$ denoted by $${\gamma _R}(G).$$ Let $$G$$ be a graph with $$V(G) = \{ {v_1},{v_2},\ldots,{v_n}\} $$ and G' be a copy of $$G$$ with $$V({G'}) = \{ v_1',v_2',\ldots,v_n'\} .$$ Then a functigraph $$G$$ with function $$\sigma :V(G) \to V({G'})$$ is denoted by $$C(G,\sigma ),$$ its vertices and edges are $$V(C(G,\sigma )) = V(G) \cup V({G'})$$ and $$E(C(G,\sigma )) = E(G) \cup E({G'}) \cup \{ v\sim {v'} | v\in V(G),{v'} \in V({G'}),\sigma (v) = {v'}\} ,$$ respectively. This paper deals with the Roman domination number of the functigraph and its complement. We present a general bound $${\gamma _R}(G) \le {\gamma _R}(C(G,\sigma )) \le 2{\gamma _R}(G),$$ where $$\sigma :V(G) \to V({G'})$$ is a permutation. Also, the Roman domination number of some special graphs are considered. We obtain a general bound of $${\gamma _R}(\overline {C(G,\sigma )} $$ and we show that this bound is sharp.

In this paper, we are concerned with the existence of the maximum and minimum iterative solutions for a tempered fractional turbulent flow model in a porous medium with nonlocal boundary conditions. By introducing a new growth condition and developing an iterative technique, we establish new results on the existence of the maximum and minimum solutions for the considered equation; at the same time, the iterative sequences for approximating the extremal solutions are performed, and the asymptotic estimates of solutions are also derived.

In the paper, we prove that the N -Kirchhoff type problem in R N has at least three solutions by using the Ekeland variational principle and fibering map.

Electrochemical reduction reaction of nitric oxide (NORR) to ammonia has been considered as a promising alternative to capturing and utilizing NO emitted from thermal-power plants. Various metal-containing catalysts have been proved to possess efficient catalytic activities for NORR, yet the attempt on metal-free NORR catalysts is quite limited. Herein, by employing first-principle calculations, we propose a novel strategy of designing metal-free NORR catalyst by introducing Ccenter-CN2 configuration into hexagonal boron nitride-graphene heterostructures (hBN-graphene). The hBN-graphene heterostructures demonstrate excellent NORR activity, achieving a fairly low limiting potential of −0.22 V. The superior NORR activity is ascribed to the introduced unique configuration at the modified hBN-graphene interface. Moreover, the hBN-graphene heterostructures can efficiently suppress hydrogen evolution—the main competitive reaction. The ab-initio molecular dynamic simulations indicate that hBN-graphene heterostructures can retain considerable thermal stability. Our work opens an avenue to design metal-free catalysts for NORR by modulating the interface in two-dimensional heterostructures.

Energy is a key factor regulated by the neuroendocrine system. The objective of this study was to compare growth performance, serum biochemical indices, carcass traits, meat quality, and nutrient composition of lambs fed restricted metabolizable energy (ME) intakes to mimic the seasonal changes of the natural grasslands of northwest China. Nineteen male Dorper × Small Tailed Han lambs were assigned to treatments, control (CON) fed at 1.0 MJ/W(0.75) × d(−1) throughout the 180 d study, and restricted ME (RES) fed by sequentially restricting ME every 30 d (0.56, 0.84, 1.0, 0.84, 0.56, and 0.28 MJ/W(0.75) × d(−1)). Lambs were harvested at the end of the study. Lambs fed the CON diet demonstrated higher (P < 0.05) average daily gain (ADG) compared with RES-fed lambs (158.79 and 57.01 g/d, for CON and RES, respectively), although ADG were lower in each period with the last period being a negative ADG for RES-fed lambs resulting in a loss of body weight. Both treatments demonstrated lower ADG in the last 3 study periods compared with the first 2 periods, which may be explained by cold stress ( 0.05) for cholesterol and high-density lipoprotein-cholesterol. Feeding lambs a restricted ME diet increased (P < 0.05) meat pH, while reducing the cooked meat rate compared with CON-fed lambs. Thus, the carcass yield, rib eye muscle area, and shear force were lower (P < 0.05) for RES-fed lambs compared with CON-fed lambs. The meat water concentration was higher (P < 0.05), whereas the concentrations of dry matter, crude fat, crude protein, and carbohydrate were lower (P < 0.05) for lambs fed a RES ME diet compared to CON-fed lambs. These results demonstrate that sequentially restricting ME intake, as natural grasslands might experience during seasonal forage quality and quantity changes, resulted in a reduction of body weight because lambs were mobilizing body reserves as a source of ME. The reduction in concentrations of key serum nutrients, as well as carcass traits and meat composition, demonstrate the body is responding to the meet the lambs ME requirements, which has implications for both meat quality and the animal’s physiological functions.

In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball. Under some suitable local growth conditions for nonlinearity, several new results are obtained by using the fixed-point theorem.

We study the existence and uniqueness of positive solution for a class of nonlinear binary operator equations systems by means of the cone theory and monotone iterative technique, under more general conditions. Also, we give the iterative sequence of the solution and the error estimation of the system. Moreover, we use this new result to study the existence and uniqueness of the solutions for fractional differential equations systems involving integral boundary value conditions in ordered Banach spaces as an application. The results obtained in this paper are more general than many previous results and complement them.

In this paper, we establish some new results on the existence and nonexistence of radial large positive solutions for a modified Schrodinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach. The necessary and sufficient condition for the existence of radial large positive solutions is established. Our results improve and extend many previous work in this field of research.

In this paper we investigate a system of impulsive integral boundary value problems with sign-changing nonlinearities. Using the fixed point theorem in double cones, we prove the existence of multiple positive solutions.