| 一类奇异二阶边值问题的正周期解 |
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| 引用本文： | 姚庆六. 一类奇异二阶边值问题的正周期解[J]. 数学学报, 2007, 50(6): 1357-136. DOI: CNKI:SUN:SXXB.0.2007-06-019 |
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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 |
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| 摘 要： | 考察了一类奇异二阶周期边值问题,其中非线性项f(t,u)是局部Caratheódory函数.主要工具是高度函数,它描述了非线性项f(t,u)在有界集合上的增长特性.通过考察高度函数的积分获得了单个或多重正解存在的几个充分条件.我们的工作表明这种存在性与非线性项f(t,u)在u=0附近的性质无关.
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| 关 键 词： | 奇异常微分方程 周期边值问题 正解 |
| 文章编号： | 0583-1431（2007）06-1357-08 |
| 收稿时间： | 2005-12-19 |
| 修稿时间： | 2005-12-09 |
Positive Periodic Solutions of a Class of Singular Second-Order Boundary Value Problems |
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| Qing Liu YAO. Positive Periodic Solutions of a Class of Singular Second-Order Boundary Value Problems[J]. Acta Mathematica Sinica, 2007, 50(6): 1357-136. DOI: CNKI:SUN:SXXB.0.2007-06-019 |
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| Authors: | Qing Liu YAO |
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| Affiliation: | Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, P. R. China |
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| Abstract: | A class of singular second-order periodic boundary value problems is con- sidered where the nonlinear term f(t,u)is a local Caratheódory function.Main tools are the height functions that describe the growth feature of nonlinear term f(t,u)on bounded set.Several sufficient conditions to guarantee the existence of single or multi- ple positive solutions are obtained by considering the integrations of height functions. Our work shows that the existence is independent of the properties of nonlinear term f(t,u)near u=0. |
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| Keywords: | singular ordinary differential equation periodic boundary value problem positive solution |
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