Multiple solutions for two classes of quasilinear problems defined on a nonreflexive Orlicz-Sobolev space

TL;DR

This paper establishes the existence and multiple solutions for certain quasilinear problems within nonreflexive Orlicz-Sobolev spaces using advanced variational methods and weak* topology properties.

Contribution

It introduces new results on solution multiplicity for quasilinear problems in nonreflexive Orlicz-Sobolev spaces, expanding the scope of variational methods.

Findings

Proved existence of solutions

Demonstrated solution multiplicity

Applied variational methods in nonreflexive spaces

Abstract

In this paper, we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz-Sobolev space. Here, we use the variational methods developed by Szulkin combined with some properties of the weak$^*$ topology.