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In this article we continue the study of discrete anisotropic equations and we will provide a new multiplicity results of the solutions for a discrete anisotropic equation. The procedure viewed here is according to variational methods and critical point theory. In fact, using a consequence of the local minimum theorem due Bonanno and mountain pass theorem we look into the existence results for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by mingling two algebraic conditions on the nonlinear term employing two consequences of the local minimum theorem due Bonanno we guarantee the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem. [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]

We provide sufficient conditions for a mappingf:Rn → Rnto be a global diffeomorphism in casefneed not be continuously differentiable. Instead it is assumed to be strictly (Hadamard-like) and Fréchet differentiable. We use classical local invertibility conditions together with the non-smooth critical point theory. [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 the Fenchel-Young duality we derive a new critical point theorem. We illustrate our results with solvability for certain discrete BVP. Multiple solutions are also considered. [ABSTRACT FROM AUTHOR]

In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters. [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 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]

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: 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]