| 非线性中立型泛函微分方程正解的迭代逼近 |
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| 引用本文： | 岳宏,刘桂荣.非线性中立型泛函微分方程正解的迭代逼近[J].太原师范学院学报(自然科学版),2013(3):1-3. |
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| 作者姓名： | 岳宏 刘桂荣 |
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| 作者单位： | 山西大学数学科学学院,山西太原030006 |
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| 基金项目： | 国家自然科学基金（11001157）;山西省高等学校优秀青年学术带头人支持计划（20120304）;山西省回国留学人员科研资助项目（2013-019）. |
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| 摘 要： | 利用Banach压缩映象原理,得到下列一阶非线性中立型泛函微分方程x(t)+a(t)x(t-τ(t))]′+f(t,x(t-σ1),x(t-σ2),…,x(t-σn))=0无穷多个有界正解的存在性.此外,还给出了这些有界正解的迭代逼近序列以及相应的误差估计.文章结果推广并改进了已有文献中的相应结果.
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| 关 键 词： | 中立型泛函微分方程 有界正解 Banach压缩映象原理 迭代逼近 |
Iterative Approximation of Positive Solutions for Nonlinear Neutral Functional Differential Equations |
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| Yue Hong Liu Guirong.Iterative Approximation of Positive Solutions for Nonlinear Neutral Functional Differential Equations[J].Journal of Taiyuan Normal University:Natural Science Edition,2013(3):1-3. |
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| Authors: | Yue Hong Liu Guirong |
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| Institution: | Yue Hong Liu Guirong (School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China) |
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| Abstract: | Using the Banach contraction mapping theorem, to prove the existence of un countably many bounded positive solutions for the first order nonlinear neutral functional differ ential equationx（t）＋a（t）z（t-r（t））]＇＋f（t,z（t-σ21））,z（t-σ1）,x（t-σn））-O In addition,to give not only the iterative approximation of the corresponding positive solutions, but also the error estimate. Our results generalize and improve some existing results. |
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| Keywords: | neutral functional differential equation bounded positive solutions Banachcontraction mapping theorem iterative approximation |
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