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).

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[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.


34K05 General theory of functional-differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations


Zbl 0727.00007