| 奇异二阶常微分方程n个正周期解的存在性 |
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| 引用本文： | 姚庆六.奇异二阶常微分方程n个正周期解的存在性[J].吉林大学学报(理学版),2007,45(2):187-192. |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | 南京财经大学 应用数学系, 南京 210003 |
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| 摘 要： | 考察二阶常微分方程u″(t)+k2u(t)=f(t,u(t))正周期解的存在性和多解性, 其中非线性项f(t,u)可以在t=0, t=2π及u=0处奇异. 通过构造适当的控制函数并利用锥上的不动点定理证明了这个常微分方程n个正周期解的存在性,其中n是任意自然数.
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| 关 键 词： | 奇异常微分方程 周期边值问题 正解 存在性 多解性 |
| 文章编号： | 1671-5489(2007)02-0187-06 |
| 收稿时间： | 2006-06-02 |
| 修稿时间： | 2006年6月2日 |
Existence of n Positive Periodic Solutions of Singular Second-order Ordinary Differential Equations |
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| YAO Qing-liu.Existence of n Positive Periodic Solutions of Singular Second-order Ordinary Differential Equations[J].Journal of Jilin University: Sci Ed,2007,45(2):187-192. |
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| Authors: | YAO Qing-liu |
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| Institution: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China |
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| Abstract: | he existence and multiplicity of positive periodic solutions are considered for the second order ordinary differential equation u″(t)+k2u(t)=f(t,u(t)), where the nonlinear term f(t,u) may be singular
att=0, t=2π and u=0. By constructing suitable control functions and using fixed point theorem on cone, the existence of npositive periodic solutions is proved for the ordinary differential equation, where n is an arbitrarynatural number. |
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| Keywords: | singular ordinary differential equation periodic boundary value problem positive solution existence multiplicity |
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