A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911281765679104 |
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| author | Matsue, Kaname |
| author_facet | Matsue, Kaname |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_02718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs Matsue, Kaname Dynamical Systems Classical Analysis and ODEs 34A26, 34C08, 34D05, 34E10, 34C41, 37C25, 58K55 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. |
| title | A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs |
| topic | Dynamical Systems Classical Analysis and ODEs 34A26, 34C08, 34D05, 34E10, 34C41, 37C25, 58K55 |
| url | https://arxiv.org/abs/2504.02718 |