Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems

Abstract

In this paper, we study discrete elliptic Dirichlet problems. Applying a variational technique together with Morse theory, we establish several results on the existence and multiplicity of nontrivial solutions. Finally, two examples and numerical simulations are provided to illustrate our theoretical results.

Keywords

• discrete elliptic dirichlet problem
• local linking
• morse theory
• nontrivial solution