The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/181254 |
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| author | Cuihua Guo Hongping Ren Shulin Sun |
| author_facet | Cuihua Guo Hongping Ren Shulin Sun |
| author_sort | Cuihua Guo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e0f5f6e1f96c478ab4c0b97c57162c47 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e0f5f6e1f96c478ab4c0b97c57162c472025-08-20T02:21:29ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/181254181254The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating NonlinearityCuihua Guo0Hongping Ren1Shulin Sun2School of Mathematical Science, Shanxi University, Taiyuan, Shanxi 030006, ChinaSchool of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, ChinaWe 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.http://dx.doi.org/10.1155/2014/181254 |
| spellingShingle | Cuihua Guo Hongping Ren Shulin Sun The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity Abstract and Applied Analysis |
| title | The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity |
| title_full | The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity |
| title_fullStr | The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity |
| title_full_unstemmed | The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity |
| title_short | The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity |
| title_sort | property of the solution about cauchy problem for fourth order schrodinger equation with critical time oscillating nonlinearity |
| url | http://dx.doi.org/10.1155/2014/181254 |
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