| 常微分方程中的几个重要不等式 |
| |
| 引用本文： | 苗静茹. 常微分方程中的几个重要不等式[J]. 辽宁师范大学学报(自然科学版), 1987, 0(2) |
| |
| 作者姓名： | 苗静茹 |
| |
| 作者单位： | 数学系 |
| |
| 摘 要： | 本文的目的是讨论常微分方程中的几个重要不等式之间的关系。我们首先是把文[4]中的微分(积分)不等式的结果从矩形域推广到条形域。并用统一的方法证明了贝尔曼不等式,格朗旺不等式和基本不等式,从而发现这三个不等式都是微分(积分)不等式的特殊情形。而且这些不等式左端的函数都是由一个一阶微分方程的初值问题的解所控制的,这样一来,本文就从两个侧面揭示了这三个不等式之间的相互关系和共同特性。
|
| 关 键 词： | Bellman不等式 Grownwall不等式 基本不等式 |
SOME IMPORTANT UNEQUALITIES OF ORDINARY DIFFERENTIAL EQUATION |
| |
| Miao jingru. SOME IMPORTANT UNEQUALITIES OF ORDINARY DIFFERENTIAL EQUATION[J]. Journal of Liaoning Normal University(Natural Science Edition), 1987, 0(2) |
| |
| Authors: | Miao jingru |
| |
| Affiliation: | Department of Matiematics Liaoning Normal University |
| |
| Abstract: | The object of this paper is to discuss the relation between some important unequalities of ordinary differential equation. First we extend the results of the differential (integral) unequality in article [4] from rettangular region into Strip region, and proved Bellman unequality, Grownwall unequality and fundamental unequality to make Use of a unitijed methed. There by discover that this three unequalities are the special case of differential (integral)unequality. Moreover the letf part funetion of this unequalities arc command by a solution of initial-value problem of certain first order differntial equatione. Thus this paper brought to light the mutual relation and common property amony these three unequalities by two aspects. |
| |
| Keywords: | Bellman unequality Grownwall unequality Fundamental unequality |
| 本文献已被 CNKI 等数据库收录！ |
