时标上的推广的Pachpatte型不等式及其在边值问题中的应用

数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 404-413.

时标上的推广的Pachpatte型不等式及其在边值问题中的应用

王五生¹, 周效良²

1.河池学院数学系广西宜州 546300|2.广东海洋大学数学系广东湛江 524088

收稿日期:2010-08-18 修回日期:2011-07-08 出版日期:2012-04-25 发布日期:2012-04-25
基金资助:
国家自然科学基金(11161018)、广西自然科学基金$(0991265)、河池学院重点课题(2009YAZ-N001)和河池学院应用数学重点学科基金(院科研[2007]2号)资助

A Generalized Pachpatte Type |Inequality on Time Scales and Application to a Boundary Value Problem

WANG Wu-Sheng¹, ZHOU Xiao-Liang²

1.Department of Mathematics, Hechi University, Guangxi Yizhou 546300;
2.Department of Mathematics, Guangdong Ocean University, Guangdong Zhanjiang 524088

Received:2010-08-18 Revised:2011-07-08 Online:2012-04-25 Published:2012-04-25
Supported by:
国家自然科学基金(11161018)、广西自然科学基金$(0991265)、河池学院重点课题(2009YAZ-N001)和河池学院应用数学重点学科基金(院科研[2007]2号)资助

摘要/Abstract

摘要：

该文利用单调化技巧研究了时标上的推广的Pachpatte型不等式, 该不等式右端有一个非常数项和三个包含未知函数与没有假设单调性的非线性函数的复合函数的积分项, 不等式左端是未知函数与非线性函数的复合函数. 所得不等式不仅把Pachpatte型不等式的离散形式和连续形式统一起来, 而且推广了已有的时标上的相应不等式. 最后, 用得到的结果研究时标上边值问题解的估计.

关键词: 不等式, 单调化, 时标, 边值问题

Abstract:

In this paper, using a technique of monotonization, the authors investigate a generalized Pachpatte type integral inequality on time scales, which includes both a non-constant term outside the integrals and three distinct nonlinear integrals without assumption of monotonicity. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known dynamic inequalities
on time scales. An application of the result to the estimation of a solution of boundary value problem on time scales is given.

Key words: Inequalities, Monotonization, Time scales, Boundary value problem

中图分类号:

34B15

王五生, 周效良. 时标上的推广的Pachpatte型不等式及其在边值问题中的应用[J]. 数学物理学报, 2012, 32(2): 404-413.

WANG Wu-Sheng, ZHOU Xiao-Liang. A Generalized Pachpatte Type |Inequality on Time Scales and Application to a Boundary Value Problem[J]. Acta mathematica scientia,Series A, 2012, 32(2): 404-413.

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