## 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.

### MSC:

 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