| 一类非线性算子方程解的存在唯一性及其应用 |
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| 引用本文： | 张晓燕,孙经先.一类非线性算子方程解的存在唯一性及其应用[J].数学物理学报(A辑),2005,25(6):846-851. |
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| 作者姓名： | 张晓燕 孙经先 |
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| 作者单位： | [1]山东大学数学与系统科学学院,济南250100 [2]徐州师范大学数学系,徐州221116 |
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| 基金项目： | 国家自然科学基金（10371066）资助 |
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| 摘 要： | 该文在更广泛的条件下,利用锥理论和Banach压缩映象原理证明了序Banach空间中一类非线性算子方程解的存在唯一性定理,并应用到Banach空间中二阶非线性混合型微分积分方程初值问题,改进并推广了已有的一些结果.
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| 关 键 词： | 锥理论 算子方程 Banach压缩映象原理 微分积分方程. |
| 文章编号： | 1003-3998(2005)06-846-06 |
| 收稿时间： | 2003-10-07 |
| 修稿时间： | 2004-12-18 |
Existence and Uniqueness of Solutions for a Class of Nonlinear Operator Equations |and its Applications |
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| ZHANG Xiao-Yan,SUN Jing-Xian. Existence and Uniqueness of Solutions for a Class of Nonlinear Operator Equations |and its Applications[J].Acta Mathematica Scientia,2005,25(6):846-851. |
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| Authors: | ZHANG Xiao-Yan SUN Jing-Xian |
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| Institution: | 1School of Mathematics and System Science, S handong University, J inan 250100; 2Department of Mathematics, Xuzhou Normal University, Xuzhou 221116 |
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| Abstract: | By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness theorem of solutions for a class of nonlinear operator equations in ordered Banach spaces are investigated in more general condition. As an application, an existence and uniqueness theorem of solutions for initial value problems of nonlinear second order integro-differential equations of mixed type in Banach spaces are given. The results presented here improve and generalize some known results. |
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| Keywords: | Cone theory Operator equation Banach Contraction mapping principle Integro-differential equation |
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