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} (-\Delta)^{ s} u-\ds\frac{ \mu u}{ |x|^{ 2s}}=|u|^{ 2^*_s-2}u+au, & \hbox{ $\text{ in}~ \Omega$},\vspace{ 0.1cm} u=0,\,\, &\hbox{ $\text{ on}~\partial \Omega$}, \\ \end{ array}% \right. \end{ equation*} provided $N>6s$, $\mu\geq0$, $0< s<1$, $2^*_s=\frac{ 2N}{ N-2s}$, $a>0$ is a constant and $\Omega$ is an open bounded domain in $\R^N$ which contains the origin.
Categories: math.AP