A time-oscillating Hartree-type Schrödinger equation
type: Item
instance of: scholarly article
title: A time-oscillating Hartree-type Schrödinger equation
zbMATH Open document ID: 1474.35582
DOI: 10.1155/2014/950132
author: Xu Chen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider the time-oscillating Hartree-type Schrödinger equation \(i u_t + \Delta u + \theta \left(\omega t\right) \left(\left|x\right|^{- \gamma} * \left|u\right|^2\right) u = 0\), 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 \(i U_t + \Delta U + I \left(\theta\right) \left(\left|x\right|^{- \gamma} * \left|U\right|^2\right) U = 0\) for their local well-posedness and global well-posedness.
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 7023381
Wikidata QID: Q59043064
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/950132
OpenAlex ID: W2126036951
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description: scientific article; zbMATH DE number 7023381