Results on multiple nontrivial solutions to partial difference equations

Abstract

In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreover, we provide five examples to illustrate applications of our theorems.

Keywords

• partial difference equation
• local linking
• morse theory
• nontrivial solution