On sequences of solutions for discrete anisotropic equations

TL;DR

This paper proves the existence of infinitely many solutions for a class of discrete anisotropic equations with a parameter, using a critical point theorem and analyzing the nonlinear terms' behavior.

Contribution

It establishes new conditions for the existence of multiple solutions without symmetry assumptions, expanding the understanding of anisotropic discrete problems.

Findings

Identified an interval of positive parameters with infinitely many solutions.

Used a recent critical point theorem to establish solution multiplicity.

Achieved results without symmetry assumptions on nonlinear data.

Abstract

Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for an anisotropic problem with a parameter is established. More precisely, a concrete interval of positive parameters, for which the treated problem admits infinitely many solutions, is determined without symmetry assumptions on the nonlinear data. Our goal was achieved by requiring an appropriate behavior of the nonlinear terms at zero, without any additional conditions.