Multiplicity of solutions for a class of quasilinear equations involving critical Orlicz-Sobolev nonlinear term

TL;DR

This paper investigates the existence and multiple solutions of quasilinear equations involving the $\

Contribution

It introduces a variational approach combined with genus theory to establish solution multiplicity for critical growth Orlicz-Sobolev problems.

Findings

Proves existence of solutions under critical growth conditions.

Establishes multiple solutions using genus theory.

Demonstrates the effectiveness of variational methods in this context.

Abstract

In this work, we study the existence and multiplicity of solutions for a class of problems involving the $\phi$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational method combined with the genus theory for even functionals.