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Abstract The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors' research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonexistence and existence of radial large positive solutions for a class of Schrödinger systems with a nonlinear random operator under certain growth conditions. We also establish the necessary and sufficient conditions for the existence of radial large positive solutions by a successive iteration technique. The results of the paper improve and extend many previous work in this field of research. [ABSTRACT FROM AUTHOR]

This paper deals with improvements of the Trudinger–Moser inequality related to the operator Q V ( u ) : = − Δ n u + V ( x ) | u | n − 2 u , where n ≥ 2 and the potential V : R n → R belongs to a class of nonnegative and continuous functions. Precisely, under suitable assumptions on V we consider the subspace E : = { u ∈ W 1 , n ( R n ) : ∫ R n V ( x ) | u | n d x < ∞ } endowed with the norm ‖ u ‖ : = [ ∫ R n ( | ∇ u | n + V ( x ) | u | n ) d x ] 1 / n and we prove that if ( u k ) is a sequence in E such that ‖ u k ‖ = 1 , u k ⇀ u ≢ 0 in E and 0 < p < p n ( u ) : = β n ( 1 − ‖ u ‖ n ) − 1 / ( n − 1 ) , then ( ⁎ ) sup k ⁡ ∫ R n Ψ ( p | u k | n / ( n − 1 ) ) d x < ∞ , where Ψ ( t ) : = e t − ∑ i = 0 n − 2 t i i ! , β n : = n ω n − 1 1 / ( n − 1 ) and ω n − 1 is the measure of the unit sphere in R n . Furthermore, p n ( u ) is sharp in the sense that there exists a sequence ( u k ) ⊂ E satisfying ‖ u k ‖ = 1 and u k ⇀ u ≢ 0 in E such that the supremum (⁎) is infinite for p ≥ p n ( u ) . As an application of the previous result we prove the following sharp form of the Trudinger–Moser inequality for the subspace E . Considering ℓ ( α ) : = sup { u ∈ E : ‖ u ‖ = 1 } ⁡ ∫ R n Ψ ∘ ν α ( u ) d x , where ν α ( u ) : = β n ( 1 + α ‖ u ‖ n n ) 1 / ( n − 1 ) | u | n / ( n − 1 ) , assuming some conditions of symmetry on V it is established (1) for 0 ≤ α < λ 1 ( V ) we have ℓ ( α ) < ∞ , (2) for α ≥ λ 1 ( V ) , ℓ ( α ) = ∞ and (3) moreover, we prove that for 0 ≤ α < λ 1 ( V ) , an extremal function for ℓ ( α ) exists. Here λ 1 ( V ) denotes the first eigenvalue of Q V ( u ) . [ABSTRACT FROM AUTHOR]

Abstract: The present paper is concerned with the convergence problem of inexact Newton methods. Assuming that the nonlinear operator satisfies the γ-condition, a convergence criterion for inexact Newton methods is established which includes Smale''s type convergence criterion. The concept of an approximate zero for inexact Newton methods is proposed in this paper and the criterion for judging an initial point being an approximate zero is established. Consequently, Smale''s α-theory is generalized to inexact Newton methods. Furthermore, a numerical example is presented to illustrate the applicability of our main results. [Copyright &y& Elsevier]

Let S = U S | S | and T = U T | T | be the polar decompositions of S and T in L ( H ) , respectively. We say that S and T have similar positive parts if | S | and | T | are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption. [ABSTRACT FROM AUTHOR]

In this paper we consider the system involving fully nonlinear nonlocal operators: { F α ( u ( x ) ) = C n , α P V ∫ R n G ( u ( x ) − u ( y ) ) | x − y | n + α d y = f ( v ( x ) ) , F β ( v ( x ) ) = C n , β P V ∫ R n G ( v ( x ) − v ( y ) ) | x − y | n + β d y = g ( u ( x ) ) . For carrying on the method of moving planes, a narrow region principle and a decay at infinity are established. Then we prove the radial symmetry and monotonicity for positive solutions to the nonlinear system in the whole space. Furthermore, non-existence of positive solutions to the nonlinear system on a half space is derived. [ABSTRACT FROM AUTHOR]

It is a natural expectation that the mathematical models of real-life phenomena have to possess some characteristic qualitative properties of the original process. For parabolic problems the main known qualitative properties are the maximum–minimum principles, nonnegativity–nonpositivity preservation and maximum norm contractivity. These properties have a fundamental relevance concerning the validity of the mathematical or numerical model: without them, the model might produce unphysical quantities that contradict reality. For linear problems with Dirichlet boundary conditions, these properties have been thoroughly investigated and their relations have been characterized. In the present paper, we extend the linear results to nonlinear problems with general boundary conditions. Firstly, we characterize various implications between the qualitative properties. Some of them are given in general, and in certain cases we restrict our study to operators with gradient-dependent principal part or to operators with heat conduction coefficient. Secondly, we give general sufficient conditions to ensure these qualitative properties, both separately and all of them together. The relations are illustrated with several examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we make it mathematically rigorous the formulation of the following quantum Schrödinger–Langevin nonlinear operator for the wavefunction in bounded domains via its mild interpretation. The a priori ambiguity caused by the presence of the multi-valued potential , proportional to the argument of the complex-valued wavefunction is circumvented by subtracting its positional expectation value, as motivated in the original derivation (Kostin, 1972 ). The problem to be solved in order to find is mostly deduced from the modulus-argument decomposition of ψ and dealt with much like in Guerrero et al. (2010) . Here ℏ is the (reduced) Planck constant, m is the particle mass, λ is a friction coefficient, is the local probability density, denotes the electric current density, and is a general operator (eventually nonlinear) that only depends upon the macroscopic observables and . In this framework, we show local well-posedness of the initial-boundary value problem associated with the Schrödinger–Langevin operator in bounded domains. In particular, all of our results apply to the analysis of the well-known Kostin equation derived in Kostin (1972) and of the Schrödinger–Langevin equation with Poisson coupling and enthalpy dependence (Jüngel et al., 2002 ). [Copyright &y& Elsevier]

Abstract: In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o.) acting on the algebra of matrices . First, we describe q.q.o. with Haar state as well as quadratic operators with the Kadison–Schwarz property. By means of such a description we provide an example of q.q.o. which is not the Kadison–Schwarz operator. Then we study stability of dynamics of q.q.o. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the existence of positive solutions for a second-order differential system by using the fixed point theorem of cone expansion and compression. [ABSTRACT FROM AUTHOR]

Abstract: A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators F in a Hilbert space is studied in this paper under less restrictive assumptions on the nonlinear operators F than the assumptions used earlier. A new method of proof of the basic results is used. An a posteriori stopping rule, based on a discrepancy-type principle, is proposed and justified mathematically under weaker assumptions on the nonlinear operator F, than the assumptions used earlier. [Copyright &y& Elsevier]

Abstract: This paper considers existence of multiple positive fixed points for some nonlinear operators, a particular case of the operators is sum of an e-concave operator and an e-convex operator. Then we apply the results to nonlinear integral equations. [Copyright &y& Elsevier]

Abstract: In this paper we provide a formulation of initial value problems for (explicit and implicit) difference equations in terms of abstract equations in sequence spaces. They will be solved using appropriate fixed point theorems and we obtain quantitative attractivity properties. [Copyright &y& Elsevier]

Abstract: In this paper, the competitor–competitor–mutualist three-species Lotka–Volterra model is discussed. Firstly, by Schauder fixed point theory, the coexistence state of the strongly coupled system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. Secondly, the existence and asymptotic behavior of T-periodic solutions for the periodic reaction–diffusion system under homogeneous Dirichlet boundary conditions are investigated. Sufficient conditions which guarantee the existence of T-periodic solution are also obtained. [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of semilinear elliptic equations in exterior domain of , . [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed point theory, under quite general condition on the nonlinear term, we obtain an existence result concerning bounded continuous nonoscillatory solutions of a second-order nonlinear difference equation with continuous variable. [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of positive solutions for the nonlinear four-point singular boundary value problem for higher-order with p-Laplacian operator. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear singular boundary value problem with p-Laplacian operator are obtained. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to introduce a generalized -concave condition, and by using Himmelberg''s fixed point theorem, to prove a new existence theorem of Nash equilibrium in non-compact generalized game with -concavity. As applications, we shall prove a minimax theorem in non-compact settings and prove a minimax inequality in compact settings. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a generalized iterative process with errors to approximate the common fixed points of two asymptotically quasi-nonexpansive mappings. A convergence theorem has been obtained which generalizes a known result. This theorem has then been used to prove another convergence theorem which, in turn, generalizes a number of results. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the density of extremal points appeared in Ekeland''s variational principle. By introducing radial intersections of sets, we give a very general result on the density of extremal points in the framework of locally convex spaces. This solves a problem proposed by G. Isac in 1997. From the general result we deduce several convenient criterions for judging the density of extremal points, which extend and improve a result of F. Cammaroto and A. Chinni. Using the equivalence between Ekeland''s variational principle and Caristi''s fixed point theorem, we obtain some density results on Caristi''s fixed points. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss Moudafi''s viscosity approximations with Meir–Keeler contractions. We first present very simple proofs of Xu''s theorems concerning Moudafi''s approximations. We next prove that Browder''s and Halpern''s type convergence theorems imply Moudafi''s viscosity approximations. Using them, we finally state several deduced theorems. [Copyright &y& Elsevier]

Abstract: In this paper we discuss some existence results and the application of quasilinearization methods, developed so far for differential equations, to the solution of the abstract problem in a Hilbert space . Under fairly general assumptions on , F and , we show that this problem has a solution that can be obtained as the limit of a quadratically convergent nondecreasing sequence of approximate solutions. If the assumptions are strengthened, we show that the abstract problem has a solution which is quadratically bracketed between two monotone sequences of approximate solutions of certain related linear equations. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the concept of τ-function which generalizes the concept of w-distance studied in the literature. We establish a generalized Ekeland''s variational principle in the setting of lower semicontinuous from above and τ-functions. As applications of our Ekeland''s variational principle, we derive generalized Caristi''s (common) fixed point theorems, a generalized Takahashi''s nonconvex minimization theorem, a nonconvex minimax theorem, a nonconvex equilibrium theorem and a generalized flower petal theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete metric spaces. We also prove that these theorems also imply our Ekeland''s variational principle. [Copyright &y& Elsevier]

Abstract: In this paper, we proved a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type and a property (E.A) introduced in [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181–188]. Our theorem generalizes Theorem 2.2 of [M. Aamri, D. El Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-Notes 3 (2003) 156–162] and Theorem 2 of [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181–188]. [Copyright &y& Elsevier]

Abstract: In this paper, we establish sufficient conditions to guarantee the existence of at least one positive solution, a unique positive solution, and multiple positive solutions for the Sturm–Liouville boundary value problem on the half-line. By using an effective operator, the fixed point theorems in cone, especially Krasnoselskii fixed point theorem, can be applied to such systems and then existence criteria are established. The interesting point of the results is that the nonlinear term f can be sign-changing. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of Banach spaces. Furthermore, we demonstrate a relationship between the weakly convergent sequence coefficient and the Jordan–von Neumann constant of a Banach space X. Using this fact, we prove that if is less than an appropriate positive number, then every multivalued nonexpansive mapping has a fixed point where E is a nonempty weakly compact convex subset of a Banach space X, and is the class of all nonempty compact convex subsets of E. [Copyright &y& Elsevier]

Abstract: In this paper, for two nonempty subsets X and Y of a linear space E, we define the class and investigate the fixed point problem for with X an almost convex subset of a locally convex space. Our fixed point theorem contains Lassonde fixed point theorem for Kakutani factorizable multifunctions as special case. [Copyright &y& Elsevier]

Abstract: In this paper, using the fixed point theorem for Kakutani factorizable multifunctions, we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies, which include the previous fixed point theorems and equilibrium existence theorems. [Copyright &y& Elsevier]

Abstract: Recently Kirk introduced the notion of asymptotic contractions on a metric space and using ultrapower techniques he obtained an asymptotic version of the Boyd–Wong fixed point theorem. In this paper we extend this result and moreover, we give a constructive proof of it. Furthermore, we obtain a complete characterization of asymptotic contractions on a compact metric space. As a by-product we establish a separation theorem for upper semicontinuous functions satisfying some limit condition. [Copyright &y& Elsevier]

The purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes. By using fixed point theorems, a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established. Under certain conditions, some existence theorems of coincidence solutions for the class of system of functional equations are shown. Some examples are given to demonstrate the advantage of our results than existing ones in the literature. [Copyright &y& Elsevier]

In this paper, φ concave-(-ψ) convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained. Moreover, some applications to nonlinear integral equations on bounded or unbounded regions are given. [Copyright &y& Elsevier]

In this paper, some multiplicity results for positive solutions of some singular semi-positone three-point boundary value problem be obtained by using the fixed point index method. [Copyright &y& Elsevier]

In this paper, we use the monotone iterative method to prove the existence of the minimal and maximal fixed points of a discontinuous strongly monotone operator on an order interval in an ordered normed linear space. As an example of the application of our results, we show the existence of extremal solutions to a class of discontinuous initial value problems. [Copyright &y& Elsevier]

This paper gives the sufficient conditions of the existence of at least three symmetric positive solutions for one type of higher order autonomous Lidstone problem by applying the five functionals fixed point theorem. The analogous result for higher order nonautonomous singular Lidstone problem is also proved here. [Copyright &y& Elsevier]

In this paper, we study the existence problem of anti-periodic solutions for the following first-order nonlinear evolution equation: u′(t)+Au(t)+F(t,u(t))=0,t∈R,u(t+T)=−u(t),t∈R, in a Hilbert space H, where A is a self-adjoint operator and F is a continuous nonlinear operator. An existence result is obtained under assumptions that D(A) is compactly embedded into H and F is anti-periodic and bounded by a L2 function. Furthermore, anti-periodic solutions for second-order equations are also studied. [Copyright &y& Elsevier]