ANNALES SOCIETATIS MATHEMATICAE POLONAE Series I: COMMENTATIONES MATHEMATICAE ROCZNIKI POLSKIEGO TOWARZYSTWA MATEMATYCZNEGO Seria I: PRACE MATEMATYCZNE XLVII (2) (2007), 207-219 Impulsive functional-differential equations of first order

Lidia Skóra
unpublished
In this paper we present some existence results for impulsive functional-differential equations of first order. 2000 Mathematics Subject Classification: 34A37, 34K45, 34K05. Key words and phrases: impulsive functional-differential equation, Volltera operator, upper and lower solutions, monotone iterative technique, global solutions. 1. Introduction. In recent years, problems with impulses have been studied by a number of authors, for example [1-5]. This work was motivated by [1],[3], where
more » ... [1],[3], where impulsive functional differential equations of first order and second order were considered. In this paper we discuss the integro-differential equations of first order with impulses at fixed moments. By the method of upper and lower solutions we obtain existence result in a sector, then using the monotone iterative scheme we prove the existence of extremal solutions. Finally, we investigate the existence and the uniqueness of the global solutions for impulsive integro-differential equations of first order. Our consideration is based on fixed point theorem.
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