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

Xiaohong Liu; Lihong Zhang; Praveen Agarwal; Guotao Wang

doi:10.1016/j.indag.2015.07.001

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

Xiaohong Liu
, Lihong Zhang
, Praveen Agarwal
, Guotao Wang

Xiamen University
Shanxi Normal University
International College of Engineering

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Indagationes Mathematicae
Volume	27
Issue number	1
DOIs	https://doi.org/10.1016/j.indag.2015.07.001
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

Discontinuous functions
Gronwall-Bellman-Bihari type inequalities
Impulsive differential systems
Integral inequalities

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10.1016/j.indag.2015.07.001

Cite this

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

abstract = "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.",

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author = "Xiaohong Liu and Lihong Zhang and Praveen Agarwal and Guotao Wang",

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T1 - On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications

AU - Liu, Xiaohong

AU - Zhang, Lihong

AU - Agarwal, Praveen

AU - Wang, Guotao

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Discontinuous functions

KW - Gronwall-Bellman-Bihari type inequalities

KW - Impulsive differential systems

KW - Integral inequalities

UR - https://www.scopus.com/pages/publications/84952987083

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DO - 10.1016/j.indag.2015.07.001

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JF - Indagationes Mathematicae

IS - 1

ER -

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

Abstract

Keywords

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