# Least energy sign-changing solution of fractional $p$-Laplacian problems involving singularities

## TL;DR

This paper establishes the existence of the least energy sign-changing solutions for a nonlocal fractional p-Laplacian problem with singularities using variational and topological methods.

## Contribution

It introduces a novel approach combining Nehari manifold, variational constraints, and Brouwer degree to handle singular nonlocal PDEs.

## Key findings

- Existence of least energy sign-changing solutions proven
- Application of Nehari manifold and degree theory to nonlocal PDEs
- Handling of singularities in fractional p-Laplacian context

## Abstract

In this paper we study the existence of a least energy sign-changing solution to a nonlocal elliptic PDE involving singularity by using the Nehari manifold method, the constraint variational method and Brouwer degree theory.