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We introduce a type of mixed variational inequality driven by a uniformly monotone operator for which we investigate the existence and uniqueness problem by applying techniques suggested in [12]. We apply the abstract results obtained to a mixed boundary value problems inspired by contact mechanics but with the elasticity operator being not necessarily strongly monotone. We allow this operator to be a uniformly monotone acting from a reflexive Banach space into its dual. [ABSTRACT FROM AUTHOR]

In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

We show that the monotonicity methods can also be applied in the fractal setting to examine existence and also existence and uniqueness. Furthermore, we investigate the continuous dependence on parameters for the problem under consideration. [ABSTRACT FROM AUTHOR]

Using the global diffeomorphism theorem we consider the existence of solutions to the following Dirichlet problem,, whereis a jointly continuous function subject to some further growth conditions. Together with a given problem we consider the family of its discretizations and as a result we prove the existence of a non-spurious solution. [ABSTRACT FROM PUBLISHER]

In this note we consider Dirichlet boundary value problem on a half line. Using critical point theory we prove the existence of at least one nontrivial solution. [ABSTRACT FROM AUTHOR]

We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the discrete p ( · ) − Laplacian on weighted finite graphs. Several auxiliary inequalities for the discrete p ( · ) − Laplacian on finite graphs are also derived. Positive solutions are considered. [ABSTRACT FROM AUTHOR]

In this note, a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one-dimensional fractional problems admits at least one non-trivial solution under an asymptotical behaviour of the nonlinear datum at zero. A concrete example of an application is then presented. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem,whereis a jointly continuous function convex inwhich does not need to satisfy any further growth conditions. [ABSTRACT FROM PUBLISHER]

We discuss the eigenvalue problem for n-th order equations with multipoint boundary conditions. We present the variational method in spite of the fact that the nonlinearity is dependent on the derivative of n/2 order. The results can be applied applied to both sublinear and superlinear cases. [ABSTRACT FROM AUTHOR]

In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function α a nonlinear term f, and a numerical parameter λ : Δ (α (k) |Δu(k - 1)|p(k - 1)-2 Δu(k - 1)) + λf(k, u(k)) = 0; k ∈ [1, T]. We derive the intervals of a numerical parameter λ for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions of the system of anisotropic discrete boundary value problems using critical point theory. We apply direct variational approach, the Ky Fan min–max inequality and the mountain pass lemma. [ABSTRACT FROM AUTHOR]

In this paper we investigate via variational methods and critical point theory the existence of solutions, uniqueness and continuous dependence on parameters to impulsive problems with ap(t)-Laplacian and Dirichlet boundary value conditions. [ABSTRACT FROM PUBLISHER]

Abstract: We investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with -Laplacian and Dirichlet type boundary conditions. We show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters. We investigate also the uniqueness of solutions. [Copyright &y& Elsevier]

Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution for anisotropic discrete Dirichlet boundary-value problems. Our results generalized and improve those in [16]. [ABSTRACT FROM AUTHOR]

Using the direct method of the calculus of variations, we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second-order discrete anisotropic equations with Dirichlet boundary conditions. [ABSTRACT FROM PUBLISHER]

Abstract: We consider the existence and multiplicity of solutions to discrete boundary value problems with the use of critical point theory combined with some monotonicity argument. We consider both sub- and super-linear problems. [Copyright &y& Elsevier]

Using monotonicity theory, we investigate the continuous dependence on parameters for the discrete BVPs, which can be written in a form of a nonlinear system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Firstly we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one nontrivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at least two nontrivial solutions. [Copyright &y& Elsevier]

Abstract: We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden–Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigating the dependence on parameters of discrete boundary value problems. [Copyright &y& Elsevier]

We investigate the dependence on parameters for second-order difference equations with two-point boundary value conditions using a variational method in case when the corresponding Euler action functional is coercive. Some applications for discrete Emden-Fowler equation are also given. [ABSTRACT FROM AUTHOR]

We improve the results of Li by using less restrictive assumptions. [ABSTRACT FROM AUTHOR]

We use direct variational method in order to investigate the dependence on parameter for the solution for a Duffing type equation with Dirichlet boundary value conditions. [ABSTRACT FROM AUTHOR]

Using critical point theory and some monotonicity results we consider the existence of solutions to a boundary value problem connected with the discrete elliptic equation with a positive parameter. [ABSTRACT FROM AUTHOR]

Abstract: Using critical point theory and monotonicity results, we consider the existence of solutions to certain types of difference equations depending on a parameter. [Copyright &y& Elsevier]

Abstract: We begin with using a dual variational method in proving the existence of solutions to a beam equation with Dirichlet boundary conditions and with a non-monotone nonlinear term. Later we investigate the dependence on a control parameter for the state equation. We find the optimal process for the optimal control problem in which the dynamics is governed by the nonlinear beam equation. [Copyright &y& Elsevier]

Abstract: We consider the existence of solutions and the continuous dependence on a parameter results for fourth-order Dirichlet problem connected with the elastic beam equation. We introduce a dual variational method. [Copyright &y& Elsevier]

Abstract: We show the existence and stability of solutions for a family of Dirichlet problems in a bounded domain and with nonconvex nonlinearity satisfying some local growth conditions. The conditions upon V and L allow for considering the -Laplacian equation. We use the relations between critical points and critical values to the primal and a suitable dual action functional to get the existence, stability and some properties of the solutions. [Copyright &y& Elsevier]

We consider the existence of solutions to the Dirichlet problem [image omitted] in case the nonlinearity satisfies local growth conditions, where [image omitted] denotes the pseudo-Laplacian with p(x)-growth. We introduce a dual variational method and provide duality relations for both action and dual action functionals that later results in the necessary and sufficient conditions for the existence of a solution. Based on these results, we obtain a sufficient condition for stability of solutions. Finally, we show that certain optimal control problem with state constraints admits a solution. [ABSTRACT FROM AUTHOR]

We provide the existence and the stability results for higher order Dirichlet problems with convex nonlinearity which satisfies general local growth conditions. We construct a dual variational method and investigate relations between primal action functional and dual action functional. [ABSTRACT FROM AUTHOR]

Abstract: We show the existence and stability of solutions for a family of Dirichlet problems with nonlinearity satisfying some local growth conditions. We construct a new duality theory which differs from the known ones in that it does not require a type of a Palais–Smale condition. [Copyright &y& Elsevier]

Abstract: We study the existence of solutions, their stability and numerical approximations for elliptic Dirichlet problems with some general growth conditions. We consider an abstract family of equations for which we derive a new variational method to obtain existence and stability results which a further applied to concrete problems. Galerkin type approximations are also obtained. [Copyright &y& Elsevier]

We study the stability and the solvability of a family of problems − (ϕ (x ′)) ′ = g (t , x , x ′ , u) + f * with Dirichlet boundary conditions, where ϕ , u, f * are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted. [ABSTRACT FROM AUTHOR]

Abstract: We undertake the question of the multiplicity of solutions to the discrete Emden–Fowler BVP by correcting some results contained in . [Copyright &y& Elsevier]