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

Abstract

In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE. \begin{align} (-Δ)^s u&= \fracλ{u^γ}+ f(x,u)~\text{in}~Ω,\nonumber u&=0~\text{in}~\mathbb{R}^N\setminusΩ,\nonumber \end{align} where $\hat{I}\text{c◯}$ is an open bounded domain in ${\mathbb{R}}^N$ with Lipschitz boundary, $N>2s$, $s\in (0,1)$, ${\hat{I}}^3\in (0,1)$. We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.

16 pages