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.
Categories: math.AP