On the Schrödinger equation with singular potentials

Abstract

We study the Cauchy problem for the non-linear Schrödinger equation with singular potentials. For point-mass potential and nonperiodic case, we prove existence and asymptotic stability of global solutions in weak-L^{p} spaces. Specific interest is give to the point-like $\delta$ and ${\delta }^{\prime }$ impurity and for two $\delta$-interactions in one dimension. We also consider the periodic case which is analyzed in a functional space based on Fourier transform and local-in-time well-posedness is proved.

Cited by in corpus (1)

• Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials