We prove the existence of a positive { \it SOLA (Solutions Obtained as Limits of Approximations)} to the following PDE involving fractional power of Laplacian \begin{ equation} \begin{ split} (-\Delta)^su&= \frac{ 1}{ u^\gamma}+\lambda u^{ 2_s^*-1}+\mu ~\text{ in}~\Omega, u&>0~\text{ in}~\Omega, u&= 0~\text{ in}~\mathbb{ R}^N\setminus\Omega. \end{ split} \end{ equation} Here, $\Omega$ is a bounded domain of $\mathbb{ R}^N$, $s\in (0,1)$, $2s<N$, $\lambda,\gamma\in (0,1)$, $2_s^*=\frac{ 2N}{ N-2s}$ is the fractional critical Sobolev exponent and $\mu$ is a nonnegative bounded Radon measure in $\Omega$.
Categories: math.AP