The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems
We study the following two-order differential equation, (Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0, where Φp(s)=|s|(p-2)s, p>0. f(x,t) and g(x,t) are real analytic functions in x and t, 2aπp- periodic in x, and quasi-periodic in t with frequencies (ω1,…,ωm). Under some odd-even property of f(...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/489148 |
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| author | Yanling Shi Jia Li |
| author_facet | Yanling Shi Jia Li |
| author_sort | Yanling Shi |
| collection | DOAJ |
| description | We study the following two-order differential equation, (Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0, where Φp(s)=|s|(p-2)s, p>0. f(x,t) and g(x,t) are real analytic functions in x and t, 2aπp- periodic in x, and quasi-periodic in t with frequencies (ω1,…,ωm). Under some odd-even property of f(x,t) and g(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense of supt∈R|x′(t)|<+∞. |
| format | Article |
| id | doaj-art-9faa5fee195541e2bc6f176c3826178b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9faa5fee195541e2bc6f176c3826178b2025-02-03T05:58:43ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/489148489148The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible SystemsYanling Shi0Jia Li1Department of Mathematics, Southeast University, Nanjing 211189, ChinaDepartment of Mathematics, Southeast University, Nanjing 211189, ChinaWe study the following two-order differential equation, (Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0, where Φp(s)=|s|(p-2)s, p>0. f(x,t) and g(x,t) are real analytic functions in x and t, 2aπp- periodic in x, and quasi-periodic in t with frequencies (ω1,…,ωm). Under some odd-even property of f(x,t) and g(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense of supt∈R|x′(t)|<+∞.http://dx.doi.org/10.1155/2011/489148 |
| spellingShingle | Yanling Shi Jia Li The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems Abstract and Applied Analysis |
| title | The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems |
| title_full | The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems |
| title_fullStr | The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems |
| title_full_unstemmed | The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems |
| title_short | The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems |
| title_sort | lagrangian stability for a class of second order quasi periodic reversible systems |
| url | http://dx.doi.org/10.1155/2011/489148 |
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