Nonlinear Ordinary Differential Equations Resolvable with Respect to an Irregular Singular Point

We define a class of systems of nonlinear ordinary differential equations, resolvable with respect to an irregular singular point, say x = ∞. It is proved that a resolvable system has a unique formal series solution in some fractional powers of x−1. Moreover, any system has a formal series solution if and only if it can be reduced to a resolvable one. We present a method of constructing a proper solution in a suitable sectorial neighorhood of infinity, which has the asymptotics in this region. The second Painleve equation is considered as an example