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

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  • 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.
    Mathematics Subject Classification: Primary: 35B35, 35Q55; Secondary: 35Q51, 35A15.

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