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arXiv · 2504.02718

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

Kaname Matsue
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Abstract

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.

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Kaname Matsue. 2025-11-24. A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs. https://arxiv.org/abs/2504.02718

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