| 二阶积分-微分方程周期边值问题正解的存在性 |
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| 引用本文： | 周媛媛,刘文斌.二阶积分-微分方程周期边值问题正解的存在性[J].吉林大学学报(理学版),2010,48(4):539-544. |
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| 作者姓名： | 周媛媛 刘文斌 |
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| 作者单位： | 1. 徐州师范大学 科文学院, 江苏 徐州 221116,2. 中国矿业大学 数学系, 江苏 徐州 221008 |
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| 摘 要： | 讨论如下一类二阶积分-微分方程周期边值问题:u″(t)+a2u(t)=f(t,u,(Su)(t)),t∈0,2π],u(0)=u(2π),u′(0)=u′(2π)正解的存在性和多重性,其中S是Fredholm积分算子.通过构造格林函数并利用锥上不动点定理证明了正解及多重正解的存在性条件.
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| 关 键 词： | 正解 积分 微分方程 周期边值问题 |
| 收稿时间： | 2009-11-09 |
Existence of Positive Solutions of Periodic Boundary Value Problems for Second Order Integro-Differential Equations |
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| ZHOU Yuan-yuan,LIU Wen-bin.Existence of Positive Solutions of Periodic Boundary Value Problems for Second Order Integro-Differential Equations[J].Journal of Jilin University: Sci Ed,2010,48(4):539-544. |
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| Authors: | ZHOU Yuan-yuan LIU Wen-bin |
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| Institution: | 1. Institute of Kewen| Xuzhou Normal University, Xuzhou 221116, Jiangsu Province, China;2. Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu Province, China |
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| Abstract: | The authors studied the existence of single and multipe positive solutions to the periodic boundary value problems (PBVP) of a class of second order integro differential equations:u″(t)+a2u(t)=f(t,u,(Su)(t)),t∈［0,2π］,u(0)=u(2π),u′(0)=u′(2π)where S is a Fredholm integral operator. By constructing Green’s function and using fixed point theorem on cone, we proved a group of conditions to gaurantee the existence and multiplicity of positive periodic solutions. |
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| Keywords: | positive solutions integro differential equations periodic boundary value problems |
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