| 一类二阶泛函微分方程多个周期解的存在性 |
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| 引用本文： | 田德生,曾宪武. 一类二阶泛函微分方程多个周期解的存在性[J]. 数学物理学报(A辑), 2010, 30(2): 525-530 |
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| 作者姓名： | 田德生 曾宪武 |
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| 作者单位： | 田德生,Tian Desheng(湖北工业大学理学院,武汉,430068);曾宪武,Zeng Xianwu(武汉大学数学与统计学院,武汉,430072) |
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| 基金项目： | 湖北工业大学科技项目 |
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| 摘 要： | 该文利用Mawhin重合度延拓定理研究了一类二阶泛函微分方程x″(t)+f(t,x(t),x(t-τ(t)))[x′(t)]~n+a(t)x~2(t)+b(t)x(t)=p(t)(n≥2)的多个周期解的问题,得到了这类方程至少存在两个周期解的结果.
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| 关 键 词： | 泛函微分方程 多个周期解 重合度 |
| 收稿时间： | 2008-02-02 |
| 修稿时间： | 2009-04-13 |
Existence of Several Perodic Solution for a Class of Second Order Functional Differential Equations |
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| TIAN De-Sheng,ZENG Xian-Wu. Existence of Several Perodic Solution for a Class of Second Order Functional Differential Equations[J]. Acta Mathematica Scientia, 2010, 30(2): 525-530 |
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| Authors: | TIAN De-Sheng ZENG Xian-Wu |
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| Affiliation: | 1.School of Science, Hubei University of Technology, |Wuhan 430068;2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072 |
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| Abstract: | By applying the continuation theorem of coincidence degree theory developed by Mawhin, the authors study the existence of several periodic solutions to the second order functional differential equation x'(t)+f(t, x(t), x(t-τ(t)))[x'(t)]n+a(t)x2(t)+b(t)x(t)=p(t)~(n ≥ 2). Some new results for the existence of at least two periodic solutions to such equation are obtained. |
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| Keywords: | Functional differential equations Sevarel periodic solutions Coincidence degree |
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