## Abstract and Applied Analysis

### A Time-Oscillating Hartree-Type Schrödinger Equation

Xu Chen

#### Abstract

We consider the time-oscillating Hartree-type Schrödinger equation ${iu}_{t}+\Delta u+\theta (\omega t)({|x|}^{-\gamma }{\ast}{|u|}^{2})u=0$, where $\theta$ is a periodic function. For the mean value $I(\theta )$ of $\theta$, we show that the solution ${u}_{\omega }$ converges to the solution of ${iU}_{t}+\Delta U+I(\theta )({|x|}^{-\gamma }{\ast}{|U|}^{2})U=0$ for their local well-posedness and global well-posedness.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 950132, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278110

Digital Object Identifier
doi:10.1155/2014/950132

Mathematical Reviews number (MathSciNet)
MR3224328

Zentralblatt MATH identifier
07023381

#### Citation

Chen, Xu. A Time-Oscillating Hartree-Type Schrödinger Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 950132, 7 pages. doi:10.1155/2014/950132. https://projecteuclid.org/euclid.aaa/1412278110

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