Multiple nodal solutions to a Robin problem with sign-changing potential and locally defined reaction

TL;DR

This paper establishes the existence of multiple nodal solutions for a Robin boundary-value problem involving a sign-changing potential and a reaction localized near zero, using advanced variational and topological methods.

Contribution

It introduces new existence results for nodal solutions in Robin problems with indefinite potentials and localized reactions, employing a combination of Morse theory and variational techniques.

Findings

Multiple nodal solutions are proven to exist.

The methods handle sign-changing potentials and localized reactions.

Results extend the theory of Robin problems with complex potentials.

Abstract

A Robin boundary-value problem with non-homogeneous differential operator, indefinite potential, and reaction defined only near zero is investigated. The existence of one or more nodal solutions is achieved by using truncation, perturbation, and comparison techniques, results from Morse theory, besides variational methods.