Averaging of integro-quasidifferential equations (Q1603167)

A quasidifferential equation is an equation of the form \[ \lim_{\Delta\to 0} \Delta^{-1} d(x(\tau+ \Delta), g(\Delta,\tau, x(\tau)))= 0 \] where \(g(.,.,.)\) is a quasimotion in a metric space. The author proves the existence theorem and the averaging of finite and infinite intervals for the following integro-quasidifferential equation with a small parameter \[ d(x(t+ \Delta,\varepsilon), Q(\Delta, t,\varepsilon t,x(t, \varepsilon),\;\int^y_{t_0} K(t, s,x(s)) ds, \varepsilon))= o(\Delta) \] and corresponding quasidifferential equation \[ d(\xi(t+\Delta, \varepsilon), q(\Delta, t,\varepsilon t,\xi(t,\varepsilon), \varepsilon))= o(\Delta). \]