| 含反馈控制和参数的非线性泛函微分系统的正周期解的分析 |
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| 引用本文： | 杜瑞霞,刘萍,罗泳.含反馈控制和参数的非线性泛函微分系统的正周期解的分析[J].数学研究,2010,43(1):1-10. |
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| 作者姓名： | 杜瑞霞 刘萍 罗泳 |
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| 作者单位： | 云南大学数学系,云南,昆明,650091 |
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| 基金项目： | supported by the projects of Science and Technology in Yunnan Province under Grant(2007A159M) |
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| 摘 要： | 我们研究下面具有反馈控制和参数的非线性微分系统的正周期解的存在性与不存在性：{dx/dt=-r（t）x（t）＋λF（t,xt,u（t-δ（t）））,du/dt=-h（t）u（t）＋g（t）x（t-σ（t））.在一定条件下通过应用Leggett．Williams不动点定理，证明该系统至少有三个正周期解；在另外的条件下，通过用反证法证明了该系统的正周期解不存在．
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| 关 键 词： | 正周期解 反馈控制 参数 锥 不动点定理 |
Analysis of Positive Periodic Solutions of Nonlinear Functional Differential System with Feedback Control and a Parameter |
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| Du Ruixia,Liu Ping,Luo Yong.Analysis of Positive Periodic Solutions of Nonlinear Functional Differential System with Feedback Control and a Parameter[J].Journal of Mathematical Study,2010,43(1):1-10. |
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| Authors: | Du Ruixia Liu Ping Luo Yong |
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| Institution: | Du Ruixia Liu Ping Luo Yong (Department of Mathematics,Yunnan University,Kunming Yunnan 650091) |
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| Abstract: | We investigate the existence and nonexistence of positive periodic solutions of nonlinear differential system with feedback control and a parameter as follow：{dx/dt=-r（t）x（t）＋λF（t,xt,u（t-δ（t）））,du/dt=-h（t）u（t）＋g（t）x（t-σ（t））.In some sufficient conditions, by employing Leggett-Williams multiple fixed point theorem, we obtained at least three positive periodic solutions; In other some sufficient conditions, by using reduction to absurdity, we prove there is no positive periodic solution. |
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| Keywords: | positive periodic solution feedback control parameter cone fixed-point theorem |
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