Maximum principle and one-sign solutions for the elliptic $p$-Laplacian

TL;DR

This paper establishes a maximum principle for the p-Laplacian with sign-changing weights and uses it to prove the existence of solutions that are either positive or negative for certain elliptic problems.

Contribution

It introduces a maximum principle for the p-Laplacian with sign-changing weights and applies it to demonstrate the existence of one-sign solutions.

Findings

Maximum principle proven for p-Laplacian with sign-changing weight

Existence of one-sign solutions established for specific elliptic problems

Method applicable to a class of quasilinear elliptic equations

Abstract

In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.