Delay differential systems with discontinuous initial data and existence and uniqueness theorems for systems with impulse and delay. (1994) - Krishna, S. V.; Anokhin, A. V.
Abstract : The main purpose of this paper is to discuss some qualitative aspects of differential equations with delays and impulses. Such systems are encountered in modeling the dynamics of prices and cultured populations. However, any such discussion has to be based on some existence and uniqueness results for delay equations with discontinuous initial data. This is the content of the first part of the paper. For an impulsive system, we observe a phenomenon of existence of infinite number of solutions subject to impulses arbitrarily close to a fixed time. Conditions, when such solutions exist and when they do not, are discussed.