Differential and Integral Equations

Generalized ODE approach to impulsive retarded functional differential equations

Márcia Federson and Štefan Schwabik

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Abstract

It is known that retarded functional differential equations (RFDEs) can be regarded as generalized ordinary differential equations (we write GODEs). See [2, 6, 7]. In this paper, we prove the equivalence between RFDEs with pre-assigned moments of impulse effects and a certain class of GODEs introduced in [8] using some ideas of [2, 6, 7]. We state results on the existence, uniqueness and continuous dependence of solutions for this class of GODEs and we use them to obtain fine results concerning the corresponding impulsive RFDEs.

Article information

Source
Differential Integral Equations, Volume 19, Number 11 (2006), 1201-1234.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050300

Mathematical Reviews number (MathSciNet)
MR2278005

Zentralblatt MATH identifier
1212.34251

Subjects
Primary: 34K05: General theory
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34A37: Differential equations with impulses 34K45: Equations with impulses

Citation

Federson, Márcia; Schwabik, Štefan. Generalized ODE approach to impulsive retarded functional differential equations. Differential Integral Equations 19 (2006), no. 11, 1201--1234. https://projecteuclid.org/euclid.die/1356050300


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