On generalized impulsive piecewise constant delay differential equations

A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsiv...

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Bibliographic Details
Published inScience China. Mathematics Vol. 58; no. 9; pp. 1981 - 2002
Main Author Chiu, Kuo-Shou
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.09.2015
Subjects
Applications of Mathematics
Constants
Delay
Differential equations
Inequalities
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Oscillations
Uniqueness theorems
分段线性
分片
唯一性定理
常微分方程
广义
积分不等式
脉冲微分方程
非线性时滞微分方程
34A36
26D10
impulsive differential equation
34K34
34K45
Green function
34K11
34K20
oscillation
Gronwall integral inequality
piecewise constant delay of generalized type
nonoscillation
stability of solutions
variation of parameters formula
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ISSN1674-7283
1869-1862
DOI10.1007/s11425-015-5010-8

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Summary:A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
Bibliography:impulsive differential equation;piecewise constant delay of generalized type;variation of parameters formula;Gronwall integral i
11-5837/O1
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-5010-8