| 常微分方程初值问题解的存在唯一性 |
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| 引用本文： | 罗环环,范胜君. 常微分方程初值问题解的存在唯一性[J]. 吉林大学学报(理学版), 2015, 53(2): 166-172 |
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| 作者姓名： | 罗环环 范胜君 |
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| 作者单位： | 中国矿业大学 理学院, 江苏 徐州 221116 |
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| 基金项目： | 国家自然科学基金(批准号:11371362);江苏省青蓝工程中青年学术带头人专项基金(批准号:苏教师[2012]39号) |
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| 摘 要： | 利用卷积逼近和Bihari不等式等工具, 在函数f(t,y)满足关于y连续、 弱单调、 具有一般增长, f(t,0)在［0,T］上绝对可积且T<+∞或T=+∞的条件下, 证明了常微分方程初值问题解的存在唯一性.
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| 关 键 词： | 常微分方程初值问题 存在唯一性 卷积逼近 Bihari不等式 |
| 收稿时间： | 2014-07-23 |
Existence and Uniqueness for the Solution of Ordinary-Differential Equations with Initial Values |
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| LUO Huanhuan , FAN Shengjun. Existence and Uniqueness for the Solution of Ordinary-Differential Equations with Initial Values[J]. Journal of Jilin University: Sci Ed, 2015, 53(2): 166-172 |
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| Authors: | LUO Huanhuan FAN Shengjun |
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| Affiliation: | College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu Province, China |
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| Abstract: | By virtue of the convolution approximation, Bihari’s inequality and other tools, we put forward and proved that the solution of the following ordinary differential equation exists and is unique under the conditions that the function f(t,y) satisfies a continuity condition, a weak monotonicity condition and a general growth condition in y, and the f(t,0) is absolutely integrable on ［0,T］ with T<+∞ or T=+∞. |
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| Keywords: | ordinary differential equation with initial value existence and uniqueness convolution approximation Bihari’s inequality |
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