| 非线性分析中的半序方法 |
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| 引用本文： | 郭大钧.非线性分析中的半序方法[J].宁夏大学学报(自然科学版),1999,20(1):5-11. |
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| 作者姓名： | 郭大钧 |
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| 作者单位： | 山东大学数学系 |
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| 基金项目： | 国家自然科学基金,国家教委博士点专项科研基金 |
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| 摘 要： | 系统论述了利用半序方法研究缺乏紧性和缺乏连续性的增算，减算以及混合单调算子最大不动点和最小不动点的存在性，不点动的存在唯一性，迭代序列的收敛性以及收敛速率估计等问题，并给出对于Ｂａｎａｃｈ空间非线性积分－微分方程的应用。文章还提出了若干提供一步研究的问题。
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| 关 键 词： | 非线性泛函分析 非线性分析 半序法 微分方程 |
Method of partial ordering in nonlinear analysis |
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| Institution: | Department of Mathematics,Harbin
Institute of Technology, Harbin 150001,China |
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| Abstract: | This paper gives a survey on the existence of maximal and minimal fixed points and existence and uniqueness of fixed points for non compact and discontinuous increasing operators, decreasing operators and mixed monotone operators by means of method of partial ordering. Convergence of iterative sequences and estimation of the convergence rate are also discussed and applications to nonlinear integro differential equations in Banach spaces are given. In addition, some problems for further investigation are offered. |
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| Keywords: | cone and partial ordering increasing and decreasing operators mixed monotone operator fixed point integro differential equation in Banach space |
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