The property of the solution about Cauchy problem for fourth-order Schrödinger equation with critical time-oscillating nonlinearity
type: Item
instance of: scholarly article
title: The property of the solution about Cauchy problem for fourth-order Schrödinger equation with critical time-oscillating nonlinearity
zbMATH Open document ID: 1470.35329
DOI: 10.1155/2014/181254
author: Cuihua Guo
author: Hongping Ren
author: Shulin Sun
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study the property of the solution in Sobolev spaces for the Cauchy problem of the following fourth-order Schrödinger equation with critical time-oscillating nonlinearity \(i u_t + \Delta^2 u + \theta(\omega t) | u |^{8 /(n - 4)} u = 0\), where \(\omega, t \in R\), \(x \in R^n\), and \(\theta\) is a periodic function. We obtain the asymptotic property of the solution for the above equation as \(\left|\omega\right| \rightarrow \infty\) under some conditions.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 7021882
Wikidata QID: Q59035818
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/181254
OpenAlex ID: W2140876219
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description: scientific article; zbMATH DE number 7021882