| 高阶微分积分方程的单调迭代法及其应用 |
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| 引用本文： | 茹静,裴明鹤.高阶微分积分方程的单调迭代法及其应用[J].纯粹数学与应用数学,2009,25(2):302-309. |
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| 作者姓名： | 茹静 裴明鹤 |
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| 作者单位： | 1. 北华大学数学学院,吉林,吉林,132013;吉林化工学院数理系,吉林,吉林,132022
2. 北华大学数学学院,吉林,吉林,132013 |
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| 摘 要： | 首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法，然后将所得结果应用到n阶微分方程的两点边值问题，得到了n阶非线性两点边值问题解的存在性及其单调迭代法，所得结果推广了已有的结果．
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| 关 键 词： | 初值问题 边值问题 单调迭代法 |
Monotone iterative technique and its application for higher order itegral-differential equations |
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| RU Jing,PEI Ming-he.Monotone iterative technique and its application for higher order itegral-differential equations[J].Pure and Applied Mathematics,2009,25(2):302-309. |
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| Authors: | RU Jing PEI Ming-he |
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| Institution: | RU Jing1,2,PEI Ming-he1 (1. Mathematics College,Beihua University,Jilin 132013,China,2. Department of Mathematics,Jilin Institute of Chemical Technology,Jilin 132022,China) |
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| Abstract: | In this paper, the existence and the monotone iterative technique of solutions of initial value problems for nth-order integral-differential equations are studied firstly by means of upper and lower solutions and differential inequality theory, then the obtained results are employed to deal with the two-point boundary value problems for nth-order differential equations, the existence and the monotone iterative technique of solutions for nth-order nonlinear two-point boundary value problems are obtained. Our... |
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| Keywords: | initial value problems boundary value problem monotone iterative technique |
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