一类一阶自治微分方程的Pu i-x级数解的存在性与收敛性
Existence and convergence of Puiseux series solutions for autonomous first order differential equations
摘要：
给出了一个自治的一阶代数常微分方程F（y，y '）=0，证明了每一个形式的Pu_x级数解，在任意有限点或无穷远处展开，都是收敛的.的证明是建设性的，我们提供了一个算法来描述所有这样的Puixix级数解。此外，我们表明，对于任何一点在复平面上存在的微分方程的解决方案，它定义了一个分析曲线通过这一点。
英文摘要：
Given an autonomous first order algebraic ordinary differential equation F(y,y')=0, we prove that every formal Puiseux series solution, expanded around any finite point or at infinity, is convergent. The proof is constructive and we provide an algorithm to describe all such Puiseux series solutions. Moreover, we show that for any point in the complex plane there exists a solution of the differential equation which defines an analytic curve passing through this point.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
