| 关于非线性边值问题几个存在性定理的新结果 |
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| 引用本文： | 吴广荣,黄文华,沈祖和,张鸿庆.关于非线性边值问题几个存在性定理的新结果[J].应用数学和力学,1999,20(1):105-109. |
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| 作者姓名： | 吴广荣 黄文华 沈祖和 张鸿庆 |
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| 作者单位： | 1. 南京大学数学系,南京,210093
2. 无锡轻工业大学,无锡,214036 |
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| 摘 要： | 本文运用同胚理论，研究微分方程边值问题解的存在性与唯一性，得到两个基本定理，推广了Ｂｒｏｗｎ（ｉｎＡｎｎａｌｉ．Ｍａｔ．Ｐｕｒａ．Ａｐｐｌｉ．１９７５，１０６：２０５～２１４）的结论，取消了有界性假设，并把我们的结果用于有限维的情况，考虑了非线性守恒系统在扰动情况下（Ｎｅｗｔｏｎ类运动方程）周期解的存在性与唯一性问题·把同胚用于这类问题的研究目前还是新的
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| 关 键 词： | 同胚 周期解 大范围反函数定理 |
New Results of Some Existence Theorems on Nonlinear Boundary Value Problems |
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| Wu Guangrong,Huang Wenhua,Shen Zuhe.New Results of Some Existence Theorems on Nonlinear Boundary Value Problems[J].Applied Mathematics and Mechanics,1999,20(1):105-109. |
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| Authors: | Wu Guangrong Huang Wenhua Shen Zuhe |
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| Affiliation: | Wu Guangrong 1 Huang Wenhua 2 Shen Zuhe 1 1 Department of Mathematics,Nanjing University,Nanjing 210093,P R China, 2 Wuxi University of Light Industry,Wuxi 214036,P R China |
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| Abstract: | With the use of the homeomorohism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniqueness of the solution obtained. The results in this note seem less restrictive than those of the former papers we have seen. Mean while, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new. |
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| Keywords: | homeomorphism existence and uniqueness global inverse theorem |
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