| 共振条件下一类方程无界解和周期解的共存性 |
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| 引用本文： | 黄国安,刘期怀.共振条件下一类方程无界解和周期解的共存性[J].纯粹数学与应用数学,2009,25(3):603-609. |
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| 作者姓名： | 黄国安 刘期怀 |
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| 作者单位： | 黄国安(桂林航天工业高等专科学校计算机系,广西,桂林,541004;广西师范大学数学科学院,广西,桂林,541004);刘期怀(苏州大学数学科学学院,江苏,苏州,215006) |
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| 摘 要： | 讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性．利用Poincare映射轨道的性质，给出了无界解的存在性条件．在此条件下，Poincare-Bohl定理，得到了方程的一个周期解，进而说明共振条件下这类方程无界解和周期解的是可以共存的．最后，给出了一个无界解和周期解共存的具有等时位势的方程实例．
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| 关 键 词： | 等时位势 无界解 周期解 共振 |
Coexistence of unbounded and periodic solutions to a class of isochronous oscillators at resonance |
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| HUANG Guo-an ,LIU Qi-huai.Coexistence of unbounded and periodic solutions to a class of isochronous oscillators at resonance[J].Pure and Applied Mathematics,2009,25(3):603-609. |
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| Authors: | HUANG Guo-an LIU Qi-huai |
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| Institution: | HUANG Guo-an 1,2,LIU Qi-huai 3 (1.Department of Computer Guilin College of Aerospace Technology,Guilin 541004,China,2.Department of Mathematics Guangxi Normal University,3.Department of Mathematics Suzhou University,Suzhou 215006,China) |
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| Abstract: | This paper studies the coexistence of unbounded and periodic solutions to a class of isochronous oscillators at resonance, obtaining the conditions of existence of unbounded solutions by the dynamics of Ponicae mapping. Under these conditions, we can get a periodic solution using Ponicae-Bohl theorem. Thus, it implies the coexistence of unbounded and periodic solutions： Finially, an example for the equations which has the coexistence of unbounded and periodic solutions is given. |
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| Keywords: | isochronous potential unbounded solutions periodic solutions resonance |
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