Existence and uniqueness of positive solution for nonlinear difference equations involving p(k)-Laplacian operator

Abstract

In this paper, we deal with the existence of at least one and of at least two positive solutions as well the uniqueness of a positive solution for an anisotropic discrete non-linear problem involving p(k)-Laplacian with Dirichlet boundary value conditions. The technical approach for the existence part is based on a local minimum theorem and on a two critical points theorem for differentiable functionals, and for uniqueness part is based on a Lipschitzian continuous condition on the nonlinearity term.

Keywords

• discrete nonlinear boundary value problem
• non trivial solution
• variational methods
• critical point theory
• primary 39a10, 39a12, 39a70
• secondary 34b15, 39f20, 65q10