On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications

被引：35

作者：

Liu, Xiaohong ^{[1
]}

Zhang, Lihong ^{[2
]}

Agarwal, Praveen ^{[3
]}

Wang, Guotao ^{[2
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Shanxi Normal Univ, Sch Math & Comp Sci, Linfen 041004, Shanxi, Peoples R China

[3] Anand Int Coll Engn, Dept Math, Jaipur 303012, Rajasthan, India

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2016年 / 27卷 / 01期

关键词：

Integral inequalities; Discontinuous functions; Gronwall-Bellman-Bihari type inequalities; Impulsive differential systems; EXPLICIT BOUNDS; TIME SCALES; EQUATIONS;

D O I：

10.1016/j.indag.2015.07.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions are established. These inequalities generalize and improve some former famous results about inequalities, and which provide an excellent tool to discuss the qualitative and quantitative properties for solutions to some nonlinear differential and integral equations. To illustrate our results, we present an example to show estimated solutions for an impulsive differential system. (C) 2015 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：1 / 10

页数：10

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