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 $\{\begin{array}{l}-\Delta u=\mu |u{|}^{2^{\star }-2}u+\frac{|u{|}^{2^{\ast }(t)-2}u}{|x{|}^t}+a(x)u\text{in}\Omega ,u=0\text{on}\partial \Omega ,\end{array}$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 $\mu \ge 0,a>0,N\ge 7,0<t<2,2^{\star }=\frac{2N}{N-2}$ and $2^{\star }(t)=\frac{2(N-t)}{N-2}$.