Sign changing solutions for quasilinear superlinear elliptic problems

TL;DR

This paper investigates the existence and multiplicity of solutions for nonlinear elliptic problems involving the $\

Contribution

It introduces new methods to find positive, negative, and nodal solutions for $\

Findings

Established existence of positive and negative ground state solutions.

Proved the existence of nodal solutions using topological methods.

Applied minimization on Nehari manifolds and topological degree theory.

Abstract

Results on existence and multiplicity of solutions for a nonlinear elliptic problem driven by the $\Phi$-Laplace operator are established. We employ minimization arguments on suitable Nehari manifolds to build a negative and a positive ground state solutions. In order to find a nodal solution we employ additionally the well known Deformation Lemma and Topological Degree Theory.