RETARDED NONLINEAR INTEGRAL INEQUALITIES OF GRONWALL-BELLMAN-PACHPATTE TYPE AND THEIR APPLICATIONS

被引：2

作者：

Shakoor, Abdul ^{[1
]}

Samar, Mahvish ^{[2
]}

Wali, Samad ^{[3
]}

Saleem, Muzammil ^{[4
]}

机构：

[1] Islamia Univ Bahawalpur, Dept Math, Bahawalpur 63100, Pakistan

[2] Zhejiang Normal Univ, Coll Math & Comp Sci, Jinhua 321004, Peoples R China

[3] Namal Univ, Dept Math, Mianwali 42250, Pakistan

[4] Aspire Grp Coll, Dept Math, Sadiq Abad Campus, Rahim Yar Khan 64200, Pakistan

来源：

HONAM MATHEMATICAL JOURNAL | 2023年 / 45卷 / 01期

关键词：

~integral inequality; retarded integral inequality; Volterra type integral equation;

D O I：

10.5831/HMJ.2023.45.1.54

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we state and prove several new retarded non-linear integral and integrodifferential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous in-equalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Appli-cations are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

引用

页码：54 / 70

页数：17

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