Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

TL;DR

This paper establishes the existence of multiple solutions for a nonlinear, non-homogeneous boundary value problem within Orlicz-Sobolev spaces, using variational methods and a Mountain Pass Lemma variant.

Contribution

It introduces a novel approach combining Orlicz-Sobolev space theory with variational techniques to find multiple solutions for complex boundary problems.

Findings

Proved existence of at least two nonnegative, non-trivial solutions.

Applied a variant of Mountain Pass Lemma in Orlicz-Sobolev spaces.

Extended variational methods to non-homogeneous boundary value problems.

Abstract

We study a non-homogeneous boundary value problem in a smooth bounded domain in $\mathbb{R}^N$. We prove the existence of at least two nonnegative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.