Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms
This paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. The solutions turn out to be, at the first order, the superposition of traveling waves...
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| Main Authors: | , , |
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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/10.1155/2014/649270 |
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| _version_ | 1832546526630510592 |
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| author | Yixian Gao Weipeng Zhang Jing Chang |
| author_facet | Yixian Gao Weipeng Zhang Jing Chang |
| author_sort | Yixian Gao |
| collection | DOAJ |
| description | This paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. The solutions turn out to be, at the first order, the superposition of traveling waves, traveling in the opposite or the same directions. The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem, while the bifurcation equations are solved by variational methods. |
| format | Article |
| id | doaj-art-545aa546f46540a188816f04fc9163ed |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-545aa546f46540a188816f04fc9163ed2025-02-03T06:48:36ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/649270649270Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced TermsYixian Gao0Weipeng Zhang1Jing Chang2School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaFundamental Department, Aviation University of Air Force, Changchun 130023, ChinaThis paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. The solutions turn out to be, at the first order, the superposition of traveling waves, traveling in the opposite or the same directions. The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem, while the bifurcation equations are solved by variational methods.http://dx.doi.org/10.1155/2014/649270 |
| spellingShingle | Yixian Gao Weipeng Zhang Jing Chang Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms Abstract and Applied Analysis |
| title | Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms |
| title_full | Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms |
| title_fullStr | Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms |
| title_full_unstemmed | Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms |
| title_short | Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms |
| title_sort | quasiperiodic solutions of completely resonant wave equations with quasiperiodic forced terms |
| url | http://dx.doi.org/10.1155/2014/649270 |
| work_keys_str_mv | AT yixiangao quasiperiodicsolutionsofcompletelyresonantwaveequationswithquasiperiodicforcedterms AT weipengzhang quasiperiodicsolutionsofcompletelyresonantwaveequationswithquasiperiodicforcedterms AT jingchang quasiperiodicsolutionsofcompletelyresonantwaveequationswithquasiperiodicforcedterms |