Abstract and Applied Analysis

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

Cuihua Guo, Hongping Ren, and Shulin Sun

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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 + Δ 2 u + θ ( ω t ) | u | 8 / ( n - 4 ) u = 0 , where ω , t R , x R n , and θ is a periodic function. We obtain the asymptotic property of the solution for the above equation as ω 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

Permanent link to this document
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


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