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A survey of differential equations with piecewise continuous arguments. (English) Zbl 0737.34045
Delay differential equations and dynamical systems, Proc. Conf., Claremont/CA (USA) 1990, Lect. Notes Math. 1475, 1-15 (1991).

[For the entire collection see Zbl 0727.00007.]

The article is a survey of the present status of the theory of differential equations with piecewise continuous arguments (EPCA). A typical EPCA is of the form x ' (t)=f(t,x(t),x(h(t)), where the argument h(t) has intervals of constancy. For example: h(t)=[t], [t-n], t-n[t], where [] denotes the greatest integer function. The main topics are: existence, uniqueness, representation and stability of the solutions; stability as a function of the delay; oscillatory and periodic solutions; approximation of equations with discrete delay; equations of alternating type and chaotic behaviour of solutions.

34K05General theory of functional-differential equations
34K99Functional-differential equations
34-02Research monographs (ordinary differential equations)