Existence and multiplicity of solutions to discrete inclusions with thep(k)-Laplacian problem

Multiple Solutions of a Discrete Nonlinear Boundary Value Problem Involving p(k)-Laplace Kirchhoff Type Operator

“…In recent years, many authors have discussed the existence and multiplicity of solutions for discrete boundary value problems by using variational methods. For the papers involving the discrete p(k)-Laplacian operator, we refer the readers to [5,21,22,23,24,29,36,38]. In the case where p(k) is a constant called the discrete p-Laplacian operator, we refer to recent works [1,2,10,11,12,13,14] and references therein.…”

Critical point approaches for discrete anisotropic Kirchhoff type problems

“…The study of discrete boundary value problems has captured special attention in the last years. The modelling of certain nonlinear problems from biological neural networks, economics models, optimal control and other areas of study have led to the rapid development of the theory of difference equations; see [3,7,8,13,18,20,21,26]. For example, Gao [8] has studied…”

Multiplicity of Solutions to Discrete Inclusions with the p(k)-Laplace Kirchhoff Type Equations

“…The remaining part of this article is organized as follows: some usefull preliminary results are presented in Section 2. In Section 3, we recall the new abstract critical point theorems established in [11], while Section 4 is devoted to the multiplicity results for problem (1.1).…”