On fractional p-Laplacian problems with weight

TL;DR

This paper studies the existence of nonnegative solutions to a nonlinear fractional p-Laplacian problem on unbounded domains, addressing challenges related to compactness in the analysis.

Contribution

It introduces new methods to handle compactness issues for fractional p-Laplacian problems with weights on unbounded domains.

Findings

Existence of nonnegative solutions established.

New techniques for compactness in fractional p-Laplacian problems.

Results applicable to weighted nonlinear problems.

Abstract

We investigate the existence of nonnegative solutions for a nonlinear problem involving the fractional p-Laplacian operator. The problem is set on a unbounded domain, and compactness issues have to be handled.