Characterization of jump discontinuities for state dependent delay differential equations

Cooke discussed the appropriateness of this model, and he presented some asymptotic theory. As early as 1960 Driver [8-111 pointed out that the two body problem of classical electrodynamics is properly modeled as an FDE with state dependent delays. Furthermore, he was (to the best of our knowledge) the first author to present an existence and uniqueness theory for such equations. The growth of interest in FDE has been stimulated by their wide-spread applications. Various forms of FDE provide the basis for mathematical models in numerous areas, including neural network theory, theory of learning, epidemiology, pharmacokinetics, and time lag control processes. For more detailed study of applications of FDE see [27]. In this paper we shall consider the scalar equation

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