On generalized impulsive piecewise constant delay differential equations

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• 作者：Kuo-Shou Chiu
• 关键词：impulsive differential equation ; piecewise constant delay of generalized type ; variation of parameters formula ; Gronwall integral inequality ; Green function ; oscillation ; nonoscillation ; stability of solutions ; 34A36 ; 34K11 ; 34K20 ; 34K34 ; 34K45 ; 26D10
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：58
• 期：9
• 页码：1981-2002
• 全文大小：403 KB
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• 作者单位：Kuo-Shou Chiu (1)
  
  1. Departamento de Matem谩tica, Facultad de Ciencias B谩sicas, Universidad Metropolitana de Ciencias de la Educaci贸n, Jos茅 Pedro Alessandri 774, Santiago, Chile
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

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.