Resonant Robin problems driven by the $p$-Laplacian plus an indefinite potential

TL;DR

This paper investigates nonlinear Robin boundary problems involving the p-Laplacian with an indefinite potential, focusing on resonance conditions and employing variational methods to establish existence and multiplicity of solutions.

Contribution

It introduces new existence and multiplicity results for p-Laplacian Robin problems under resonance conditions with indefinite potentials.

Findings

Proved existence of solutions under strong resonance.

Established multiplicity results using variational methods.

Analyzed the impact of indefinite potentials on solution behavior.

Abstract

We consider a nonlinear Robin problems driven by the $p$-Laplacian plus an indefinite potential. The reaction is resonant with respect to a variational eigenvalue. For the principal eigenvalue we assume strong resonance. Using variational tools and critical groups we prove existence and multiplicity theorems.