Advances in Differential Equations

Infinite energy solutions for Schrödinger-type equations with a nonlocal term

Vanessa Barros and Ademir Pastor

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We study the Cauchy problem associated with nonlinear Schrödinger-type equations with a nonlocal term in $\mathbb{R}^n$. Existence and uniqueness of local and global solutions are established in spaces which allow singular initial data. Scattering, asymptotic stability, and decay rates are also proved.

Article information

Adv. Differential Equations, Volume 18, Number 7/8 (2013), 769-796.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35C06: Self-similar solutions 35E15: Initial value problems 35Q35: PDEs in connection with fluid mechanics 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]


Barros, Vanessa; Pastor, Ademir. Infinite energy solutions for Schrödinger-type equations with a nonlocal term. Adv. Differential Equations 18 (2013), no. 7/8, 769--796.

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