Solutions for a nonlocal elliptic equation involving critical growth and Hardy potential

In this paper, by an approximating argument, we obtain infinitely many solutions for the following Hardy-Sobolev fractional equation with critical growth \begin{equation*}\label{0.1} \left\{% \begin{array}{ll} (-Δ)^{s} u-\ds\frac{μu}{|x|^{2s}}=|u|^{2^*_s-2}u+au, & \hbox{$\text{in}~ Ω$},\vspace{0.1cm} u=0,\,\, &\hbox{$\text{on}~\partial Ω$}, \\ \end{array}% \right. \end{equation*} provided $N>6s$, $μ\geq0$, $0< s<1$, $2^*_s=\frac{2N}{N-2s}$, $a>0$ is a constant and $Ω$ is an open bounded domain in $\R^N$ which contains the origin.

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