On a nonlocal multivalued problem in an Orlicz-Sobolev space via Krasnoselskii's genus

TL;DR

This paper investigates multiple solutions for a nonlocal problem within Orlicz-Sobolev spaces, utilizing Krasnoselskii's genus and locally Lipschitz functionals, advancing the understanding of solution multiplicity in complex functional settings.

Contribution

It introduces a novel approach combining Krasnoselskii's genus with nonlocal Orlicz-Sobolev problems, addressing solution multiplicity with new theoretical insights.

Findings

Established existence of multiple solutions

Applied Krasnoselskii's genus in a nonlocal Orlicz setting

Extended solution theory to locally Lipschitz functionals

Abstract

This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz-Sobolev space for a nonlocal problem involving N-functions and theory of locally Lispchitz continuous functionals.