Infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annulus

TL;DR

This paper proves the existence of infinitely many solutions to the Dirichlet problem involving the p-Laplacian in annular domains, especially when p is less than or equal to N, by addressing compactness issues through variable change.

Contribution

It introduces a novel approach to establish multiple solutions for the p-Laplacian Dirichlet problem in annuli when p ≤ N, overcoming compactness challenges.

Findings

Proved existence of infinitely many solutions in annular domains.

Addressed compactness failure of Sobolev spaces via variable change.

Applicable for p ≤ N in the p-Laplacian context.

Abstract

We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\leq N$, contouring the failure of compactness of $W^{1,p}(\Omega)$ in $C^0(\bar{\Omega})$ applying a variable change.