Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 214, pp. 1-12.

Title: Ground state solutions for semilinear problems with a Sobolev-Hardy term

Authors: Xiaoli Chen  (Jiangxi Normal Univ., Nanchang, Jiangxi, China)
         Weiyang Chen (Jiangxi Normal Univ., Nanchang, Jiangxi, China)

Abstract:
 In this article, we study the existence of solutions to the  problem
 $$\displaylines{
 -\Delta u= \lambda u+\frac{|u|^{2_s^\ast-2}u}{|y|^s}, \quad x\in  \Omega,\cr
 u = 0,  \quad x\in  \partial \Omega,
 }$$
 where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$ $(N\geq3)$.
 We show that there is a ground state solution provided that N=4 and
 $\lambda_m<\lambda<\lambda_{m+1}$,
 or that $N\geq 5$ and $\lambda_m\leq\lambda<\lambda_{m+1}$, where
 $\lambda_m$ is the m'th eigenvalue of $-\Delta$ with Dirichlet boundary
 conditions.

Submitted  April 19, 2013. Published September 26, 2013.
Math Subject Classifications: 35J60, 35J65.
Key Words: Existence; ground state; critical Hardy-Sobolev exponent;
           semilinear Dirichlet problem.