The sign-changing solutions for singular critical growth semilinear elliptic equations with a weight

Abstract

By means of variational method, we study a singular critical growth semilinear elliptic problem: $-\Delta{u}=Q(x)|u|^{2^*-2}{u}+\mu \frac{u}{|x|^2}+\lambda u,$ $u\in H^1_0(\Omega)$, where $2^*=\frac{2N}{N-2},$ $N\geq 7,$ $0 <\mu <\frac{(N-2)^2}{4},$ $\lambda>0$, and $Q(x)$ is a positive function on $\overline{\Omega}$. By investigating the effect of the coefficient of the critical nonlinearity, we prove the existence of sign-changing solutions.