A new continuous dependence result for impulsive retarded functional differential equations

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• 作者：Márcia Federson ; Jaqueline Godoy Mesquita
• 关键词：retarded functional differential equation ; impulse local existence ; impulse local existence uniqueness ; continuous dependence on parameters
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：66
• 期：1
• 页码：1-12
• 全文大小：142 KB
• 参考文献：[1] M. Federson, J. G. Mesquita: Averaging principle for functional differential equations with impulses at variable times via Kurzweil equations. Differ. Integral Equ. 26 (2013), 1287–1320.MathSciNet MATH
  [2] M. Federson, J. G. Mesquita: Averaging for retarded functional differential equations. J. Math. Anal. Appl. 382 (2011), 77–85.MathSciNet CrossRef MATH
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  [8] V. Lakshmikantham, D. D. Baĭnov, P. S. Simeonov: Theory of Impulsive Differential Equations. Series in Modern Applied Mathematics Vol. 6, World Scientific, Singapore, 1989.CrossRef MATH
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• 作者单位：Márcia Federson (1)
  Jaqueline Godoy Mesquita (2)
  
  1. Instituto de Ciências Matemáticas e de Computaçcão, Universidade de São Paulo, Campus de São Carlos, Avenida Trabalhador São Carlense, 400, Caixa Postal 668, 13560-970, São Carlos-SP, Brazil
  2. Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte, 70910-900, Brasília-DF, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141

文摘

We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the limiting equation is an impulsive RFDE whose initial condition is the uniform limit of the sequence of the initial data and whose solution exists and is unique. Then, for sufficient large indexes, the elements of the sequence of impulsive retarded initial value problem admit a unique solution and such a sequence of solutions converges to the solution of the limiting Cauchy problem.