Algebraic systems with Lipschitz perturbations

TL;DR

This paper proves the existence of infinitely many solutions for nonlinear algebraic systems with Lipschitz perturbations using variational methods, under specific conditions on the nonlinear term without symmetry assumptions.

Contribution

It introduces a novel approach to establish solution existence in algebraic systems with Lipschitz perturbations without relying on symmetry conditions.

Findings

Infinitely many solutions exist for the studied systems.

Variational methods are effective in handling Lipschitz perturbations.

Conditions on the nonlinear term are sufficient for solution existence.

Abstract

By using variational methods, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established in presence of a perturbed Lipschitz term. Our goal was achieved requiring an appropriate behavior of the nonlinear term $f$, either at zero or at infinity, without symmetry conditions.