Multiple solutions for a inclusion quasilinear problem with non-homogeneous boundary condition through Orlicz Sobolev spaces

TL;DR

This paper extends recent mathematical results to prove the existence of three solutions for a quasilinear inclusion problem with non-homogeneous boundary conditions using Orlicz Sobolev spaces, broadening the understanding of such nonlinear problems.

Contribution

It introduces a new application of critical point theory to establish multiple solutions for quasilinear problems in Orlicz Sobolev spaces, expanding previous work to include non-smooth functionals and non-homogeneous boundaries.

Findings

Proves the existence of three solutions to the problem.

Extends critical point theory to non-smooth functionals.

Applies Orlicz Sobolev spaces to quasilinear problems.

Abstract

In this work we estend a recent result of Krist\'aly, Marzantowicz and Varga concerning the existence of three critical points certain non-smooth functionals. Using this result, we guarantee the existence of three solutions to a inclusion quasilinear problem, with non-homogeneous boundary condition through Orlicz Sobolev spaces.