Necessary and sufficient conditions for finite time singularities in ordinary differential equations
نویسندگان
چکیده
Necessary and sufficient conditions for the existence of finite time singularities for the general solution of systems of ordinary differential equations are given. The systems of ordinary differential equations under consideration form a large subset of the set of all autonomous, nonlinear polynomial ordinary differential equation. The conditions for finite time blowup involve a reality condition on the leading term of the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithmically. Examples are given.
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