论文标题
标量准线性普通微分方程的单数初始值问题
Singular Initial Value Problems for Scalar Quasi-Linear Ordinary Differential Equations
论文作者
论文摘要
我们讨论了标量准线性的普通微分方程的初始值问题和两侧解决方案的存在，非唯一性和规律性，其中初始条件对应于方程的僵局。通过差异几何方法，我们将问题减少到动态系统理论中的问题。作为一个应用程序，我们详细讨论了$ g（x）u''= f（x，u，u'）$的二阶方程，并以$ g $的简单零征用初始条件。这是梁的总体结果，还通过我们的几何方法使它们更加透明。
We discuss existence, non-uniqueness and regularity of one- and two-sided solutions of initial value problems for scalar quasi-linear ordinary differential equations where the initial condition corresponds to an impasse point of the equation. With a differential geometric approach, we reduce the problem to questions in dynamical systems theory. As an application, we discuss in detail second-order equations of the form $g(x)u''=f(x,u,u')$ with an initial condition imposed at a simple zero of $g$. This generalises results by Liang and also makes them more transparent via our geometric approach.
