Asymptotic properties of solutions of nonlinear vector initial value problem on the infinite interval

In this paper we study initial value problems on the infinite interval: where x, f∈E^m, y, g∈Eⁿ,εare real small positive parameters,0≤t<+∞. On condition that g_y(t) is nonsingular and under other assumptions, we have proved that there areserial (k+m*) -dimensionalmanifolds {S_R(ε)}∈^m+n such that (1.1) degenerates regularly provided(ξ(ε),η(ε))∈S_R(ε). Besides, the R-order asymptotic expansions of solutions are constructed, and their errors are estimated.