Bifurcation for nonlinear elliptic problems with singular potentials (Q2022252)

Bifurcation for the following elliptic problem with singular potentials \[ \left \{ \begin{array}{ll} -\Delta u-\frac{(N-2)^2u}{4|x|^2}= \frac{\lambda f(u)}{|x|^{\beta}}& \mbox{ in }\Omega, \\ u = \, 0 \ & \mbox{ on }\ \partial \Omega, \end{array} \right. \] where \(\Omega\) is a smooth bounded domain in \(\mathbb R^N\) containing the origin with \(N\ge 3\), \(0<\beta<1\), and \(\lambda\) is a real parameter, is studied under certain conditions on the real function \(f\).