| 关于微分方程局部解存在定理证明的注记 |
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| 引用本文： | 葛莉,姚云飞.关于微分方程局部解存在定理证明的注记[J].阜阳师范学院学报(自然科学版),2013,30(1):77-80. |
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| 作者姓名： | 葛莉 姚云飞 |
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| 作者单位： | 阜阳师范学院数学和计算科学学院,安徽阜阳,236037 |
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| 基金项目： | 安徽省高校优秀人才基金项目 |
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| 摘 要： | 通过对有关微分方程局部解存在定理经典证明的研究,给出了一个强化条件下的局部解存在定理,同时给出了一个一阶常微分方程解存在的简化证明和解的一般表达式,并提出教学建议。
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| 关 键 词： | 微分方程 局部解 存在定理 几何模型 |
A note on the existence theorem of local solution for differential equation |
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| GE Li
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YAO Yun-fei.A note on the existence theorem of local solution for differential equation[J].Journal of Fuyang Teachers College:Natural Science,2013,30(1):77-80. |
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| Authors: | GE Li YAO Yun-fei |
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| Institution: | (School of Mathematica and Computational Science, Fuyang Teachers College, Fuyang Anhui 23637, China) |
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| Abstract: | Based on the classic proof of the existence theorem of local solution for differential equation, an existence theorem under a reinforcement condition is presented. And then we provide both simplified proof of the solution existence for first order differential equations and a general expression for the solution. Finally, some teaching suggestinns are proposed. |
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| Keywords: | differential equation local solution existence theorem geometrical model |
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