标题： 非自治常微分方程中无穷远处动力学描述的爆破解的简单说明 显示英文标题

标题： A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs

摘要： 关于非自治常微分方程（类型-I）爆破解的存在性的一个简单判据被给出。 在之前的研究[Matsue, SIADS, 24(2025), 415-456]中，通过无穷远处的动力学，提供了用于表征非自治常微分方程爆破解的几何判据。朝着当前目标的基本思想是将这些判据对应于与爆破解假设相关的主导项方程，该假设用于描述源自自治常微分方程框架中的相应研究的多阶渐近展开。 将注意力限制在爆破解主导项系数的常数上，可以模仿自治常微分方程中爆破解特征的简单判据到非自治常微分方程中。 显示英文摘要

摘要： A simple criterion of the existence of (type-I) blow-up solutions for nonautonomous ODEs is provided. In a previous study [Matsue, SIADS, 24(2025), 415-456], geometric criteria for characterizing blow-up solutions for nonautonomous ODEs are provided by means of dynamics at infinity. The basic idea towards the present aim is to correspond such criteria to leading-term equations associated with blow-up ansatz characterizing multiple-order asymptotic expansions, which originated from the corresponding study developed in the framework of autonomous ODEs. Restricting our attention to constant coefficients of leading terms of blow-ups, results involving the simple criterion of blow-up characterizations in autonomous ODEs can be mimicked to nonautonomous ODEs.