Existence results for singular critical elliptic problems in \(\mathbb R^N\) (Q2465847)

The author considers the semilinear elliptic equation with critical Sobolev-Hardy exponents: \[ -\triangle u-\frac{\mu}{| x| ^{2}}u+\lambda V(x)u=K(x)\frac{| u| ^{2^{*}(s)-2}}{| x| ^{s}}u\quad\text{in }\mathbb R^{N}, \] where \( N\geq 3\), \(0\leq\mu<\overline{\mu}:= (\frac{N-2}{2})^{2}\), \(\lambda>0\), \(0\leq s<2\), \(2^{*}(s)=\frac{2(N-s)}{N-2}\). The author proves by means of a linking theorem that under suitable conditions the problem has at least one nontrivial solution.