Differential and Integral Equations

Maximum decay rate for finite-energy solutions of nonlinear Schrödinger equations

Pascal Bégout

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Abstract

We give explicit time lower bounds in the Lebesgue spaces for all nontrivial solutions of nonlinear Schrödinger equations bounded in the energy space. The result applies for these equations set in any domain of $\mathbb R^N,$ including the whole space. This also holds for a large class of nonlinearities, thereby extending the results obtained by Hayashi and Ozawa in [9] and by the author in [2].

Article information

Source
Differential Integral Equations Volume 17, Number 11-12 (2004), 1411-1422.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060253

Mathematical Reviews number (MathSciNet)
MR2100034

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Bégout, Pascal. Maximum decay rate for finite-energy solutions of nonlinear Schrödinger equations. Differential Integral Equations 17 (2004), no. 11-12, 1411--1422. https://projecteuclid.org/euclid.die/1356060253.


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