Triple solutions for a Dirichlet boundary value problem involving a perturbed discrete p(k)-Laplacian operator

Abstract

Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p.k/-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Riccerilocal minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

Existence of two solutions for a fourth-order difference problem with p(k) exponent

“…It is well known that variational method and critical point theory are important tools to deal with the problems for differential equations. Recently, the existence and multiplicity of solutions for nonlinear discrete boundary value problems have been investigated by adopting variational methods (see [2,12,15] ).…”