Existence and Multiplicity of Positive Solutions for Quasilinear Elliptic Systems Involving the P-Laplacian

TL;DR

This paper investigates the existence and multiple positive solutions for a class of quasilinear elliptic systems involving the P-Laplacian operator, utilizing variational methods on the Nehari manifold.

Contribution

It establishes the existence of at least two distinct nonnegative solutions for the system using fibering maps and Palais-Smale sequences.

Findings

Proves existence of multiple solutions under certain conditions.

Utilizes fibering maps and Nehari manifold techniques.

Identifies at least two nontrivial solutions.

Abstract

We study the existence and multiplicity of solutions to the elliptic system where RN is a bounded and smooth domain. Using fibering maps and extracting Palais-Smale sequences in the Nehari manifold, we prove the existence of at least two distinct nontrivial nonnegative solutions.