A note on the well posed anisotropic discrete BVP's

TL;DR

This paper investigates the existence, uniqueness, and parameter dependence of solutions to second order discrete anisotropic boundary value problems using variational methods.

Contribution

It applies the direct calculus of variations method to analyze discrete anisotropic BVPs, providing new insights into their solution properties.

Findings

Established conditions for existence and uniqueness

Proved continuous dependence on parameters

Extended analysis to anisotropic discrete equations

Abstract

Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.