Аннотация:We propose the hypothesis that the local integrability in sense (1)
in all stationary points of autonomous planar systems of ordinary
differential equations with polynomial right sides and resolved
with respect to derivatives leads to existence of the global first
integral if this system has these local integrability at the same sets
of parameters. If the system has invariant curves or separatists such integral can
exist only in a part of the phase space.