Quasilinear elliptic equations in $\RN$ via variational methods and Orlicz-Sobolev embeddings

TL;DR

This paper establishes the existence of nontrivial non-negative radial solutions for quasilinear elliptic equations in RN using variational methods within Orlicz-Sobolev spaces, and also demonstrates multiple solutions.

Contribution

It introduces a variational approach in Orlicz-Sobolev spaces to find solutions and proves multiplicity results for quasilinear elliptic equations.

Findings

Existence of a nontrivial non-negative radial solution

Multiple solutions are established

Application of critical points theory in Orlicz-Sobolev spaces

Abstract

In this paper we prove the existence of a nontrivial non-negative radial solution for a quasilinear elliptic problem. Our aim is to approach the problem variationally by using the tools of critical points theory in an Orlicz-Sobolev space. A multiplicity result is also given.