Superlinear perturbations of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential

TL;DR

This paper investigates a superlinear perturbation of the Robin Laplacian eigenvalue problem with an indefinite potential, demonstrating the existence of multiple solutions near certain eigenvalues using variational methods.

Contribution

It introduces a novel analysis of the Robin Laplacian with an unbounded indefinite potential, establishing the existence of multiple solutions near nonprincipal eigenvalues.

Findings

Seven nontrivial solutions near certain eigenvalues.

Sign information provided for six solutions.

Application of variational tools and critical groups.

Abstract

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when $\lambda$ is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.