# Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity

## TL;DR

This paper proves the existence of infinitely many positive weak solutions for a nonlocal elliptic PDE with a singular term, using variational methods within a bounded domain.

## Contribution

It establishes the existence of infinitely many solutions for a nonlocal PDE involving singularity, which is a novel result in this context.

## Key findings

- Infinitely many positive weak solutions exist.
- Solutions are obtained via variational techniques.
- The PDE involves a singular term with specific parameter constraints.

## Abstract

In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE. \begin{align} (-\Delta)^s u&= \frac{\lambda}{u^{\gamma}}+ f(x,u)~\text{in}~\Omega,\nonumber u&=0~\text{in}~\mathbb{R}^N\setminus\Omega,\nonumber \end{align} where $\Omega$ is an open bounded domain in $\mathbb{R}^N$ with Lipschitz boundary, $N>2s$, $s\in (0,1)$, $\gamma\in (0,1)$. We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.