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Zbl 0737.34045
Cooke, Kenneth L.; Wiener, Joseph
A survey of differential equations with piecewise continuous arguments. (English)
[A] 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.]\par 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.
[G.Derfel (Beer-Sheva)]

MSC 2000:: *34K05 General theory of functional-differential equations
34K99 Functional-differential equations
34-02 Research monographs (ordinary differential equations)

Keywords: functional-differential equations; piecewise constant lag; survey; existence; uniqueness; representation; stability; oscillatory and periodic solutions; approximation; equations of alternating type; chaotic behaviour; differential equations with piecewise continuous arguments

Citations: Zbl 0727.00007

Cited in: Zbl 0876.34079

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