一类推广的二变量和差分不等式及其在初边值问题中的应用

数学物理学报 ›› 2013, Vol. 33 ›› Issue (2): 340-353.

一类推广的二变量和差分不等式及其在初边值问题中的应用

王五生¹|李自尊²|周效良³

1.河池学院数学系广西宜州 546300|2.百色学院数学与计算机信息工程系广西百色 533000|3.广东海洋大学数学系广东湛江 524088

收稿日期:2011-10-10 修回日期:2012-12-03 出版日期:2013-04-25 发布日期:2013-04-25
基金资助:
国家自然科学基金(11161018)、广西自然科学基金(0991265, 2012GXNSFAA053009)、广西教育厅科学研究基金(201106LX599, 201204LX423 )和广东省自然科学基金(10452408801004217)资助

A New Generalized Sum-Difference Inequality with Two Variables and Applications to BVP

WANG Wu-Sheng¹, LI Zi-Zun², ZHOU Xiao-Liang³

1,Department of Mathematics, Hechi University, Guangxi Yizhou |546300|2.Department of Mathematics and Computer Science, Baise University, Guangxi Baise 533000|3.Department of Mathematics, Guangdong Ocean University, Guangdong Zhanjiang 524088

Received:2011-10-10 Revised:2012-12-03 Online:2013-04-25 Published:2013-04-25
Supported by:
国家自然科学基金(11161018)、广西自然科学基金(0991265, 2012GXNSFAA053009)、广西教育厅科学研究基金(201106LX599, 201204LX423 )和广东省自然科学基金(10452408801004217)资助

摘要/Abstract

摘要：

建立了一个二变量的和差分不等式, 该不等式不仅右端和号外的项是非常数项, 而且包含k项未知函数和非线性函数的复合函数; 运用单调化技巧和强单调概念给出了不等式中未知函数的上界估计; 所得结果可以用来估计 Cheung W S (2006) 和王五生(2008)所研究的不等式中的未知函数; 最后, 用研究不等式得到的结果研究二变量差分方程初边值问题的有界性、唯一性和连续依赖性.

关键词: 和差分不等式, 单调化, 强单调性, 有界性

Abstract:

In this paper, we establish a general form of sum-difference inequality in two variables, which contains both a nonconstant term outside the sums and k terms of nonlinear sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities considered in the work of Cheung W S (2006) and Wang W S (2008). Furthermore, we apply our result to a boundary value problem of a partial difference equation for boundedness, uniqueness and continuous dependence.

Key words: Sum-difference inequality, Monotonization, Stronger nondecreasing, Boundedness

中图分类号:

39A10

王五生, 李自尊, 周效良. 一类推广的二变量和差分不等式及其在初边值问题中的应用[J]. 数学物理学报, 2013, 33(2): 340-353.

WANG Wu-Sheng, LI Zi-Zun, ZHOU Xiao-Liang. A New Generalized Sum-Difference Inequality with Two Variables and Applications to BVP[J]. Acta mathematica scientia,Series A, 2013, 33(2): 340-353.

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