A note on fractional $p$-Laplacian problems with singular weights

TL;DR

This paper investigates fractional p-Laplacian problems with potentially singular boundary weights, establishing existence, multiplicity, and critical group characterizations, with applications in nonlinear analysis.

Contribution

It introduces new results on existence and multiplicity for fractional p-Laplacian problems with boundary singular weights, including critical group analysis.

Findings

Existence of solutions under singular boundary weights

Multiple solutions established for certain conditions

Characterization of critical groups related to the problem

Abstract

We study a class of fractional $p$-Laplacian problems with weights which are possibly singular on the boundary of the domain. We provide existence and multiplicity results as well as characterizations of critical groups and related applications.