| 非线性一阶常微分方程解的存在惟一性 |
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| 引用本文： | 蒋玲芳. 非线性一阶常微分方程解的存在惟一性[J]. 纯粹数学与应用数学, 2012, 0(2): 256-261 |
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| 作者姓名： | 蒋玲芳 |
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| 作者单位： | 西北师范大学数学与信息科学学院,甘肃兰州730070 |
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| 基金项目： | 国家自然科学基金(10671158);甘肃省自然科学基金(3ZS051-A25-016) |
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| 摘 要： | 讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理.
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| 关 键 词： | 一阶非线性微分方程 存在性 惟一性 Leray-Schauder非线性抉择 Banach不动点定理 |
Existence and uniqueness of solutions for first-order nonlinear ordinary differential equations |
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| Jiang Lingfang. Existence and uniqueness of solutions for first-order nonlinear ordinary differential equations[J]. Pure and Applied Mathematics, 2012, 0(2): 256-261 |
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| Authors: | Jiang Lingfang |
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| Affiliation: | Jiang Lingfang(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China) |
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| Abstract: | In this paper,we show the existence and uniqueness of solutions of first-order nonlinear ordinary differential equation boundary value problem.The sufficient conditions for the existence and uniqueness of solu-tions are obtained when the parameter belongs to appropriate intervals,and we include some known results.The main results are based upon Leray-Schauder nonlinear alternative theorem and Banach’s fixed point theorem. |
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| Keywords: | first-order nonlinear differential equation existence uniqueness Leray-Schauder nonlinear alternative Banach’s fixed point theorem |
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