*(English)*Zbl 0737.34045

[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 ${x}^{\text{'}}\left(t\right)=f(t,x\left(t\right),x\left(h\left(t\right)\right)$, where the argument $h\left(t\right)$ has intervals of constancy. For example: $h\left(t\right)=\left[t\right]$, $[t-n]$, $t-n\left[t\right]$, where $\left[\phantom{\rule{4pt}{0ex}}\right]$ 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 |

34-02 | Research monographs (ordinary differential equations) |