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 Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

Keywords

• discrete boundary value problem
• p(k)-laplacian
• three solutions
• variational methods
• critical point theory
• 39a10
• 39a12
• 39a70
• 34b15
• 65q10