On a discrete elliptic problem with a weight

TL;DR

This paper investigates a discrete elliptic boundary value problem with a weight function, applying variational methods and critical point theory to establish conditions for the existence of solutions depending on a parameter.

Contribution

It introduces new existence criteria for solutions of weighted discrete elliptic problems using variational and critical point techniques.

Findings

Established multiple criteria for solution existence

Demonstrated solution dependence on a real parameter

Applied variational methods to discrete elliptic problems

Abstract

Using the variational approach and the critical point theory, we established several criteria for the existence of at least one nontrivial solution for a discrete elliptic boundary value problem with a weight $p(\cdot, \cdot)$ and depending on a real parameter $\lambda$.