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July/August 2014 On the Schrӧdinger equation with singular potentials
Lucas C.F. Ferreira, Jaime Angulo Pava
Differential Integral Equations 27(7/8): 767-800 (July/August 2014).

Abstract

We study the Cauchy problem for the non-linear Schrӧdinger equation with singular potentials. For the point-mass potential and nonperiodic case, we prove existence and asymptotic stability of global solutions in weak-$L^{p}$ spaces. Specific interest is given to the point-like $\delta$ and $\delta'$ impurity and to 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.

Citation

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Lucas C.F. Ferreira. Jaime Angulo Pava. "On the Schrӧdinger equation with singular potentials." Differential Integral Equations 27 (7/8) 767 - 800, July/August 2014.

Information

Published: July/August 2014
First available in Project Euclid: 6 May 2014

zbMATH: 1340.35319
MathSciNet: MR3200763

Subjects:
Primary: 35A05, 35A07, 35B10, 35B40, 35C15, 35Q55

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 7/8 • July/August 2014
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