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

2025/04/03 by Kaname Matsue, Matsue, Kaname
Mathematics · #34A26 #34C08 #34C41 #34D05 #34E10 #37C25 #58K55 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2504.02718

openalex publication_date 2025/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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