Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents (Q1766475)

The authors obtain the existence of nontrivial solutions for the singular critical problem \[ -\Delta u- \mu{u\over |x|^2}= {|u|^{2^*(s)- 2}\over|x|^2}+\lambda u\quad\text{in }\Omega,\;u= 0\quad\text{on }\partial\Omega, \] where \(\Omega\subset\mathbb{R}^N\) is a smooth bounded domain in such that \(0\in\Omega\), \(N\geq 3\), \(0\leq s< 2\), \(2^*(s)= {2(N-s)\over N-2}\), \(\lambda\) and \(\mu\) are positive parameters.