Local Properties of Stationary Solutions of some Nonlinear Singular Schr6dinger Equations

Abstract

We study the local behaviour of solutions of the following type of equation $–\Delta u–V(x)u+g(u)=0$ when $V$ is singular at some points and $g$ is a non-decreasing function. Emphasis is put on the case when $V(x)=clx{l}^{–2}$ and $g$ has a power-like growth.