Multiplicity of solutions for gradient systems under strong resonance at the first eigenvalue

TL;DR

This paper proves the existence and multiple solutions for a strongly resonant elliptic system at the first eigenvalue using variational methods and indefinite weight eigenvalue problems.

Contribution

It introduces new results on multiplicity of solutions for elliptic systems with strong resonance at the first eigenvalue, employing variational techniques and indefinite weights.

Findings

Existence of solutions established.

Multiple solutions demonstrated.

Use of indefinite weight eigenvalue problem.

Abstract

In this paper we establish existence and multiplicity of solutions for an elliptic system which has strong resonance at first eigenvalue. To describe the resonance, we use an eigenvalue problem with indefinite weight. In all results we use Variational Methods.