## Abstract and Applied Analysis

### The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity

#### Abstract

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 $i{u}_{t}+{\mathrm{\Delta }}^{2}u+\theta (\omega t)|u{|}^{8/(n-4)}u=0$, 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 $|\omega |\to \infty$ under some conditions.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 181254, 14 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277127

Digital Object Identifier
doi:10.1155/2014/181254

Mathematical Reviews number (MathSciNet)
MR3246317

Zentralblatt MATH identifier
07021882

#### Citation

Guo, Cuihua; Ren, Hongping; Sun, Shulin. The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity. Abstr. Appl. Anal. 2014 (2014), Article ID 181254, 14 pages. doi:10.1155/2014/181254. https://projecteuclid.org/euclid.aaa/1412277127