On an elliptic problem with critical exponent and Hardy potential (Q652463)

The authors study the following elliptic problem with critical exponent and a Hardy potential: \(-\Delta u-\frac{\mu}{|x|^2}u=\lambda u+|u|^{2^*-2}u\), \(u\in H^1_0(\Omega)\), where \(\Omega\) is a smooth open bounded domain in \(R^N\). The authors show that, if \(N\geq 5\) and \(\mu>0\) is sufficiently small, then the problem has a ground state solution for each \(\lambda>0\) and, if \(N\geq 7\), then the problem has infinitely many sign-changing solutions for every \(\lambda>0\).