Differential and Integral Equations
- Differential Integral Equations
- Volume 19, Number 11 (2006), 1201-1234.
Generalized ODE approach to impulsive retarded functional differential equations
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  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.
Differential Integral Equations, Volume 19, Number 11 (2006), 1201-1234.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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