| Benson方法及其应用 |
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| 引用本文： | 王书枢,王挽澜. Benson方法及其应用[J]. 成都大学学报(自然科学版), 2006, 25(1): 4-6,24 |
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| 作者姓名： | 王书枢 王挽澜 |
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| 作者单位： | 成都市社保局,四川,成都,610075;成都大学,计算机科学与技术系,四川,成都,610106 |
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| 摘 要： | 首先讨论Benson方法的优点与缺点,然后对于涉及n次连续可微的函数u(x)使用简明的Benson程序建立相关的积分微分不等式.例如,我们有(下面定理3):假设v(x)是区间[a,b]上n阶连续可微函数,它的n阶导数v(n)(x)0,且Q(v(n-1),L,v,′v,x)和G(v(n-1),L,v,′v,x)对v(n-1)的偏导数Gv(n-1)均为连续可微的正值函数,那么,当0
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| 关 键 词： | Benson方法 不等式 推广 |
| 文章编号： | 1004-5422（2006）01-0004-04 |
| 收稿时间： | 2005-07-12 |
| 修稿时间： | 2005-07-12 |
Benson's Method and Its Applications |
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| WANG Shushu,WANG Wanlan. Benson's Method and Its Applications[J]. Journal of Chengdu University (Natural Science), 2006, 25(1): 4-6,24 |
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| Authors: | WANG Shushu WANG Wanlan |
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| Affiliation: | 1. The Social Insurance Bureau of Chengdu, Chengdu 610106, China; 2. Department of Computer Science and Technology, Chengdu University, Chengdu 610106,China |
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| Abstract: | First of all,we discuss that Benson's method has both strong and weak points.By means of "Benson's programming",then we establish the related integro-differential inequalities involving an ntimes continuously differentiable function u(x).For example,we have(Theorem 3):Let v(x) be an n-times continuously differentiable function on with v~((n))(x)0,let Q(v~((n-1)),L,v′,v,x) and G(v~((n-1)),L,v′,v,x) be continuously differentiable positive functions.If 0
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| Keywords: | Benson's method inequality generalization. |
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