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    Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves
January  2008, 21(1): 121-136. doi: 10.3934/dcds.2008.21.121

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

1. 

Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

2. 

Equipe de Mathématiques (UMR CNRS 6623), Université de Franche-Comté, 16 Route de Gray, 25030 Besançon

Received  December 2006 Revised  March 2007 Published  February 2008

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 $H^1(\R, \C)$, but not on all $H^1(\R, \C)$, and study its orbital stability.
Citation: Reika Fukuizumi, Louis Jeanjean. Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 121-136. doi: 10.3934/dcds.2008.21.121
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