Generalized ODE approach to impulsive retarded functional differential equations

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.