Stability Results of Solution of Non-Homogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation

被引：0

作者：

Igobi, D. K. ^{[1
]}

Igbinosun, Lucky ^{[1
]}

Atsu, Jeremiah ^{[2
]}

机构：

[1] Univ Uyo, Dept Math, PMB 1017, Uyo, Nigeria

[2] Cross River Univ Technol, Calabar, Nigeria

来源：

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS | 2021年 / 12卷 / 02期

关键词：

Generalized ordinary differential equation; Regulated function; Fundamental matrix solution; Kurzweil integral; Bounded variation; Stability; asymptotic stability; TOPOLOGICAL DYNAMICS;

D O I：

10.26713/cma.v12i2.1436

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work is devoted to the study of a non-homogeneous impulsive retarded equation with bounded delays and variable impulse time using the generalized ordinary differential equations (GODEs). The integral solution of the system satisfying the Caratheodory and Lipschitz conditions obtained using the fundamental matrix theorem is embedded in the space of the generalized ordinary differential equations and investigate the problem of stability of the system in the Lyapunov sense. In particular, results on the necessary and sufficient conditions for stability and asymptotic stability of the impulsive retarded system via the generalized ordinary differential equation are obtained. An example is used to illustration the derived theory.

引用

页码：379 / 400

页数：22

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