Singular extremal solutions for supercritical elliptic equations in a ball (Q1643164)

This paper deals with the existence of positive singular solutions for Dirichlet elliptic problems of the type \(\Delta u+\lambda f(u)=0\) in the unit ball of \({\mathbb R}^N\). It is assumed that the reaction \(f\) is of the form \(f(u)=u^p+g(u)\), with \(p\) supercritical exponent and \(g\) being a lower order term. The authors obtain various qualitative properties, such as the uniqueness of the singular solution and the existence of singular extremal solutions. Also they obtain a necessary and sufficient condition for the existence of the singular extremal solution in terms of the weak eigenvalue of the linearized problem. The proofs combine variational and topological arguments.