Weak solutions for discrete Kirchhoff type equations with Dirichlet boundary conditions

Abstract

This paper is concerned with the existence and multiplicity of weak solutions for discrete Kirchhoff type equations with Dirichlet boundary conditions. We first establish the existence of a nontrivial weak solution and three weak solutions, by using variational methods, mainly based on the mountain pass theorem of A. Ambrosetti and P.H. Rabinowitz and critical point theory.