Systems of differential equations of infinite order with small parameter and countable Markov chains

Tikhonov-type Cauchy problems are investigated for systems of ordinary differential equations of infinite order with a small parameter µ and initial conditions. It is studying the singular perturbated systems of ordinary differential equations of infinite order of Tikhonov-type µẋ = F (x(t, gx),y(t, gy),t), ẏ = f(x(t, gx),y(t, gy),t) with the initial conditions x(t0)=gx, y(t0)=gy,wherex, gx ∈ X, X ⊂ l1 and y, gy ∈ Y, Y ∈ Rn, t ∈ [t0,t1](t0 <t1), t0,t1 ∈ T, T ∈ R, gx and gy are given vectors, µ>0 is a small real parameter. The results may be applied to the queueing networks, which arise from the modern telecommunications. © Springer International Publishing AG 2016.