On some variational algebraic problems

TL;DR

This paper uses critical point theory to prove the existence of two distinct solutions for a nonlinear algebraic system with a parameter, with applications to difference equations.

Contribution

It introduces a novel approach leveraging critical point theory to establish solution multiplicity for algebraic systems with parameter dependence.

Findings

Proved existence of two solutions under specific conditions.

Applied results to difference equations.

Demonstrated the effectiveness of critical point methods.

Abstract

In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the nonlinear term $f$ at zero and at infinity. Some applications to difference equations are also presented.