Differential and Integral Equations

On the Schrӧdinger equation with singular potentials

Lucas C.F. Ferreira and Jaime Angulo Pava

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 7/8 (2014), 767-800.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1399395752

Mathematical Reviews number (MathSciNet)
MR3200763

Zentralblatt MATH identifier
1340.35319

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35A05 35A07 35C15: Integral representations of solutions 35B40: Asymptotic behavior of solutions 35B10: Periodic solutions

Citation

Pava, Jaime Angulo; Ferreira, Lucas C.F. On the Schrӧdinger equation with singular potentials. Differential Integral Equations 27 (2014), no. 7/8, 767--800. https://projecteuclid.org/euclid.die/1399395752


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