Strauss- and Lions-type results for a class of Orlicz-Sobolev spaces and applications

TL;DR

This paper establishes Strauss and Lions-type compactness results for Orlicz-Sobolev spaces and applies them to prove the existence of solutions for certain quasilinear problems in Euclidean space.

Contribution

It introduces new Strauss and Lions-type theorems tailored for Orlicz-Sobolev spaces, extending classical results to this broader functional setting.

Findings

Proved Strauss-type compactness result for Orlicz-Sobolev spaces

Established Lions-type concentration-compactness principle in this context

Applied these results to demonstrate solution existence for quasilinear PDEs

Abstract

The main goal this work is to prove two results like Strauss and Lions for Orlicz-Sobolev spaces. After, we use these results for study the existence of solutions for a class of quasilinear problems in $\mathbb{R}^{N}$.