Multiple solutions for a weighted $p$-Laplacian problem

TL;DR

This paper establishes the existence of at least three solutions for a weighted p-Laplacian boundary value problem using advanced mathematical theorems in reflexive Banach spaces.

Contribution

It introduces a new application of a three solution theorem to a weighted p-Laplacian problem, demonstrating the existence of multiple solutions.

Findings

Proved the existence of at least three solutions.

Applied a three solution theorem in a weighted Sobolev space.

Extended the understanding of solution multiplicity in nonlinear PDEs.

Abstract

We prove the existence of at least three solutions for a weighted $p$-Laplacian operator involving Dirichlet boundary condition in a weighted Sobolev space. The main tool we use here is a three solution theorem in reflexive Banach spaces due to G. Bonanno and B. Ricceri.