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

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 iut + Δ2u + θ(ωt) | u|8/(n−4)u = 0, where ω, t ∈ R, x ∈ Rn, and θ is a periodic function. We obtain the asymptotic property of the solution for the above equation as |ω| → ∞ under some conditions.

Date: 2014
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https://doi.org/10.1155/2014/181254

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:181254

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