| 完全非线性三阶微分方程周期解的存在性 |
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| 引用本文： | 王晓燕,李彦刚.完全非线性三阶微分方程周期解的存在性[J].宁夏大学学报(自然科学版),2013(4):294-297. |
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| 作者姓名： | 王晓燕 李彦刚 |
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| 作者单位： | 兰州工业学院基础学科部,甘肃兰州730050 |
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| 基金项目： | 国家自然科学基金资助项目（71002037） |
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| 摘 要： | 借助Fourier分析的方法及非线性项的扰动技巧,利用Leray-Schauder不动点定理,获得了完全非线性三阶微分方程u'(t)=f(t,u(t),u′(t),u″(t)),t∈Rω-周期解的存在性及唯一性,其中f:R×R×R×R→R连续,关于t以ω为周期.
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| 关 键 词： | 完全非线性微分方程 周期解 Leray-Schauder不动点定理 |
Existence of Periodic Solutions for Fully Third-order Nonlinear Ordinary Differential Equation |
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| Wang Xiaoyan,Li Yangang.Existence of Periodic Solutions for Fully Third-order Nonlinear Ordinary Differential Equation[J].Journal of Ningxia University(Natural Science Edition),2013(4):294-297. |
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| Authors: | Wang Xiaoyan Li Yangang |
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| Institution: | 1.Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, China;) |
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| Abstract: | With the aid of the method of Fourier analysis and the perturbation technique of nonlinear term,the existence and uniqueness of ω-periodic solutions for the following fully third-order nonlinear ordinary differential equation is obtained by Leray-Schauder fixed point theorem,u（＂＇）（t） =f（t,u（t）,u＇ （t）,u＂（t））,t ∈ R,where f：R × R × R × R→R is a continuous function and is ω-periodic in t. |
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| Keywords: | fully nonlinear differential equation periodic solutions Leray-Schauder fixed point theorem |
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