| 常微分方程初始函数问题及其解的约束极值 |
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| 引用本文： | 吴新元.常微分方程初始函数问题及其解的约束极值[J].南京大学学报(自然科学版),1987(2). |
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| 作者姓名： | 吴新元 |
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| 作者单位： | 南京大学数学系 |
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| 摘 要： | 本文讨论一类与古典常微分方程求解相反的问题。已知常微分方程(组)要求在某种条件下确定其初始条件,我们你之为常微分方程初始函数问题(常微分方程中的另一类反问题见3])。全文讨论了常微分方程初始函数问题解的存在性,唯一性与连续可微性,进而讨论了初始函数问题解的约束极值问题,介绍了求解这类问题的数值方法及应用。
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| 关 键 词： | 常微分方程 反问题 极值 |
INITIAL FUNCTION PROBLEM OF ORDINARY DIFFERENTIAL EQUATIONS AND THE CONSTRAINED EXTREME VALUE OF ITS SOLUTION |
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| WU XINYUAN.INITIAL FUNCTION PROBLEM OF ORDINARY DIFFERENTIAL EQUATIONS AND THE CONSTRAINED EXTREME VALUE OF ITS SOLUTION[J].Journal of Nanjing University: Nat Sci Ed,1987(2). |
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| Authors: | WU XINYUAN |
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| Institution: | Mathematics Department |
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| Abstract: | This paper discusses a type of problem in contrast to that wick Solves the classical ordinary differential equation, suppose the ordinary differential equation is known. It is necessary to determine the initial conditions along with certain constrained conditions. We call this problem the initial function problem of ordinary differential equations(another type is the inverse problem, see3]). the paper also deals with the existence, unidueness, continuity and differentiability of the initial function problem of ordinary differential equations, and the costrained extreme value of their solutions with certain constrained conditions. In addition, a numerical method for solving this problem and its application are presented as well. |
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| Keywords: | ODE Inverse Extremum |
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