Remarks on singular critical growth elliptic equations
Shuangjie Peng · Discrete and Continuous Dynamical Systems · 2006
Let $\Omega$ be a bounded domain in $\mathbb R^N$$(N\geq 4)$with smooth boundary $\partial \Omega$ and the origin $0 \in\overline{\Omega}$, $\mu*=2N/(N-2). We obtain existenceresults of positive and sign-changing solutions to Dirichletproblem $-\Delta u=\mu\frac{ u}{|x|^2}$+|u|2*-2u+$\lambda u \ \text{on}\ \Omega,\ u=0\ \text{on}\ \partial\Omega$, which also gives a positiveanswer to the open problem proposed by A. Ferrero and F. Gazzolain [Existence of solutions for singular critical growth semilinearelliptic equations, J. Differential Equations, 177(2001),494-522].