On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential (Q2502551)

Summary: We present some results concerning the problem \[ -\Delta u=\lambda \frac{u}{x^2}+u^q,\quad u>0\text{ in }\Omega,\quad u|_{\partial\Omega}=0, \] where \(0<q<(N+2)/(N-2)\), \(q\neq 1\), \(\lambda\geq 0\) and \(\Omega\) is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.