一类二阶自治微分方程的代数曲线解的存在性问题

The Existence of Algebraic Curve Solutions for a Class of Second Order Autonomous Differential Equations

本文考虑了一类二阶自治系统的代数曲线解的存在性问题.利用整除定理给出了这类系统不具有代数曲线解的几个条件;证明了如果这类系统是Liouville可积的,则一定有代数曲线解.

In the paper,the existence of algebraic curve solutions of a class of two order autonomous system is considered.The conditions of the system having no algebraic curve solutions are given by using Division theorem.The system has algebraic curve solutions if the system is Liouville integrability,the result is presented.