Distributional solutions of the stationary nonlinear Schrödinger equation: singularities, regularity and exponential decay

Rainer Mandel, Wolfgang Reichel

We consider the nonlinear Schrödinger equation $-\Delta u+V(x)u=\Gamma (x)|u{|}^{p-1}u$ in ${\mathbb{R}}^n$ where the spectrum of $-\Delta +V(x)$ is positive. In the case $n\ge 3$ we use variational meth…