Multiplicity of Solutions for Quasilinear Elliptic Problems

TL;DR

This paper investigates the existence, uniqueness, and multiplicity of solutions for quasilinear elliptic problems involving the -Laplacian operator, using variational methods and auxiliary problems.

Contribution

It extends the analysis of quasilinear elliptic problems to both reflexive and nonreflexive cases with new variational techniques.

Findings

Established existence, uniqueness, and multiplicity of solutions.

Applied variational methods, regularity results, and truncation techniques.

Addressed both reflexive and nonreflexive cases.

Abstract

It is established existence, uniqueness and multiplicity of solutions for a quasilinear elliptic problem problems driven by $\Phi$-Laplacian operator. Here we consider the reflexive and nonreflexive cases using an auxiliary problem. In order to prove our main results we employ variational methods, regularity results and truncation techniques.