On the nonexistence and existence of solutions for a fourth-order discrete Dirichlet boundary value problem

Abstract

This paper is concerned with a class of fourth-order nonlinear difference equations. By using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for a Dirichlet boundary value problem and give some new results. Results obtained generalize and complement the existing ones.

Keywords: Nonexistence and existence, Dirichlet boundary value problem, fourth-order, mountain pass lemma, discrete variational theory.