Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and Hardy-Sobolev exponent

Abstract: We study the existence and multiplicity of sign changing solutions of the following equation $ \begin{cases} -\Delta u = \mu |u|^{2^{\star}-2}u+\frac{|u|^{2^{*}(t)-2}u}{|x|^t}+a(x)u \quad\text{in}\quad \Omega, u=0 \quad\text{on}\quad\partial\Omega, \end{cases} $where $\Omega$ is a bounded domain in $R^N$, $0\in\partial\Omega$, all the principal curvatures of $\partial\Omega$ at $0$ are negative and $\mu\geq 0, \ \ a>0, \ \ N\geq 7, \ \ 0<t<2, \ \ 2^{\star}=\frac{2N}{N-2}$ and $2^{\star}(t)=\frac{2(N-t)}{N-2}$.