Non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian

Abstract

We investigate the non-trivial solutions for a partial discrete Dirichlet nonlinear problem with $ p $-Laplacian by applying Ricceri's variational principle and a two non-zero critical points theorem. In addition, we identify open intervals of the parameter $ \lambda $ under appropriate constraints imposed on the nonlinear term. This allows us to ensure that the nonlinear problem has at least one or two non-trivial solutions.

Keywords

• partial discrete nonlinear problem
• critical point theory
• $ p $-laplacian
• non-trivial solutions