Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac

We consider a stationary nonlinear Schröodinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of $H^1(\R, ... View More