| 奇异一阶周期系统正解的存在性 |
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| 引用本文： | 张丽娟.奇异一阶周期系统正解的存在性[J].数学的实践与认识,2008,38(22). |
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| 作者姓名： | 张丽娟 |
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| 作者单位： | 白城师范学院,数学系,吉林,白城,137000 |
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| 基金项目： | 国家自然科学基金
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| 摘 要： | 主要研究了具有奇异一阶周期系统正解的存在性,证明了一阶周期系统在点(x,y)=(0,0)处具有奇异性时,在一些合理的条件下,此问题正解的存在性.证明主要依赖非线性Leray-Schauder抉择定理和Krasnoselskii锥不动点定理,同时在证明过程中格林函数也起了非常重要的作用.
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| 关 键 词： | 奇异 周期问题 正解 Krasnoselskii锥不动点定理 Leray-Schauder抉择定理 |
The Existence Positive Solutions of First Order Singular Periodic Systems |
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| ZHANG Li-juan.The Existence Positive Solutions of First Order Singular Periodic Systems[J].Mathematics in Practice and Theory,2008,38(22). |
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| Authors: | ZHANG Li-juan |
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| Institution: | Department of Mathematics;Baicheng Normal College;Baicheng 137000;China |
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| Abstract: | We are devoted to establish the positive solutions of first order singular periodic systems.It is proved that such a problem may be singular at point (x,y)=(0,0),the existence solutions is obtained under our reasonable conditions.The existence of positive solutions is obtained.The proof relies on a nonlinear alternative of Leray-Schauder theorem and Krasnoselskii fixed point theorem in cones.The green function is also important in the proof. |
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| Keywords: | singular periodic problem positive solution Leray-Schauder alternative theorem Krasnoselskii fixed point theorem in cones |
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