Averaging of functional-differential inclusions. (Russian) Zbl 0717.34080

Bulgakov, A. I.

Differ. Uravn. 26, No. 10, 1678-1690 (1990).

As is known from a paper of V. A. Plotnikov [Mat. Zametki 27, 947- 952 (1980; Zbl 0442.34014)], in systems of differential equations or differential inclusios of standard type it is possible to carry out a partial averaging, i.e. to average certain factors or other terms from the right-hand sides of the equations or inclusions. Such a way of using the averaging method turns out to be useful in cases where average values of certain functions do not exist. In this paper a method of partial averaging for functional-differential inclusions is proposed. It represents a generalization of the Krylov-Bogolyubov averaging method for ordinary differential equations to functional-differential inclusions with bounded or unbounded aftereffects.

MSC:

34K99	Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34A60	Ordinary differential inclusions
34C29	Averaging method for ordinary differential equations

Keywords:

partial averaging; Krylov-Bogolyubov averaging method; unbounded aftereffects