| Logistic型方程周期解和概周期解的存在性 |
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| 引用本文： | 祝文壮,冀书关,刘柏枫.Logistic型方程周期解和概周期解的存在性[J].东北数学,2007,23(4):298-310. |
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| 作者姓名： | 祝文壮 冀书关 刘柏枫 |
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| 作者单位： | [1]School of Mathematics, Peking University, Beijing, 100871 [2]College of Mathematics, Jilin University, Changchun, 130012 [3]Shandong Institute of Business and Technology, Yantai, 264005 |
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| 摘 要： | In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.
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| 关 键 词： | 周期解 假设推理法 概周期解 逻辑斯谛方程式 |
| 文章编号： | 1000-1778（2007）04-0298-13 |
| 收稿时间： | 2006-07-10 |
The Existence of Periodic and Almost Periodic Solutions of Logistic Type Equation |
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| ZHU Wen-zhuang,JI Shu-guan,LIU Bai-feng.The Existence of Periodic and Almost Periodic Solutions of Logistic Type Equation[J].Northeastern Mathematical Journal,2007,23(4):298-310. |
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| Authors: | ZHU Wen-zhuang JI Shu-guan LIU Bai-feng |
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| Institution: | 1. School of Mathematics, Peking University, Bejing, 100871;2. College of Mathematics, Jilin University, Changchun, 130012;3. Shandong Institute of Business and Technology, Yantai, 264005 |
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| Abstract: | In this paper, we study the Logistic type equation x= a(t)x - b(t)x2 e(t). Under the assumptions that e(t) is small enough and a(t), b(t) are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a(t), b(t) and e(t)are periodic functions, and this solution is an almost periodic solution if a(t), b(t)and e(t) are almost periodic functions. |
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| Keywords: | Logistic type equation periodic solution almost periodic solution |
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