| 一类二阶三点边值问题单调正解的存在性 |
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| 引用本文： | 刘锡平,贾梅,葛渭高.一类二阶三点边值问题单调正解的存在性[J].应用数学学报,2007,30(1):111-119. |
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| 作者姓名： | 刘锡平 贾梅 葛渭高 |
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| 作者单位： | 1. 上海理工大学理学院,上海,200093
2. 北京理工大学应用数学系,北京,100081 |
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| 摘 要： | 利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．
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| 关 键 词： | 三点边值问题 锥上不动点定理 单调正解 凹凸性 |
| 修稿时间： | 2005-05-25 |
Existence of Monotone Positive Solutions to a Type of Three-point Boundary Value Problem |
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| LIU XIPING,JIA MEI,GAO WEIGAO.Existence of Monotone Positive Solutions to a Type of Three-point Boundary Value Problem[J].Acta Mathematicae Applicatae Sinica,2007,30(1):111-119. |
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| Authors: | LIU XIPING JIA MEI GAO WEIGAO |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093;Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081 |
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| Abstract: | This paper studies the existence of monotone positive solutions to a type of three point boundary value problems of nonlinear second-order differential equations. By use of the stretch and compression fixed point theorem of normic form in cone, the sufficient conditions for the existence of monotone positive solutions are given to the boundary value problems with homogeneous and nonhomogeneous boundary conditions, respectively. An example is also given to illustrate the effectiveness of our results. |
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| Keywords: | three-point boundary value problem the fixed point theorem in cone monotone positive solutions concavity |
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