| 一类一阶常微分方程初值问题的无穷多解性 |
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| 引用本文： | 王海玲,张志军.一类一阶常微分方程初值问题的无穷多解性[J].数学学习,2010,13(4):27-28. |
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| 作者姓名： | 王海玲 张志军 |
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| 作者单位： | 烟台大学数学与信息科学学院,山东烟台264005 |
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| 基金项目： | 国家自然科学基金项目，山东省自然科学基金项目 |
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| 摘 要： | 应用分离变量法,得到了一类一阶微分方程初值问题u′(t)=b(t)f(u(t)),t0,u(0)=0存在无穷多个解的充分必要条件.并给出了全部解.
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| 关 键 词： | 一阶非线性微分方程 初值问题 无穷多解 |
Multi-solutions to a Class of First Order Ordinary DE with Initial Value |
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| WANG Hai Ling,ZHANG Zhi Jun.Multi-solutions to a Class of First Order Ordinary DE with Initial Value[J].Studies In College Mathematics,2010,13(4):27-28. |
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| Authors: | WANG Hai Ling ZHANG Zhi Jun |
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| Institution: | (School of Mathematics and Informational Science, Yantai University,Yantai, Shandong, 264005, PRC) |
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| Abstract: | From the variable-separating method and inverse function theorem, a sufficient and necessary condition for the existence of infinitely many solutions to a class of first order ordinary differential equations, u′（t）=b（t）f（u））,t〉0, with initial value, u（0）=0, is derived. Some ex4mples are show here and their all solutions are given. |
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| Keywords: | first order differential equations initial value problems infinitely many solutions |
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