Necessary and sufficient conditions for finite time singularities in ordinary differential equations

This paper gives a theorem which provides necessary and sufficient conditio ns for the existence of a real finite value of the independent variable at which the general solution of a certain class of ordinary differential equa tions diverges to infinity. This class is a large subset of the set of all autonomous, non-linear polynomial ordinary differential equation. These con ditions involve the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithm ically. (C) 2000 academic Press.