Alberto Lastra, Pascal Remy, Maria Suwinska
Abstract:
In this article we focus on the formal solutions for some regular
Gevrey-type differential equation, with convergence of such solutions being the main
point of interest. The attained results are a generalization of the classical result
on the convergence of formal solutions to differential equations.
The technique applied rests upon a classical argument based on a precise writing of
the formal solution and a dilatation, in which several technical results on general
properties of Gevrey-type sequences and Gevrey-type differential operators are applied.
Submitted February 21, 2026. Published May 12, 2026.
Math Subject Classifications: 34A34, 34A25, 34M25.
Key Words: Power series; convergence; formal solution; Gevrey-type differential equation;
Gevrey-type sequence
DOI: 10.58997/ejde.2026.36
Show me the PDF file (364 KB), TEX file for this article.
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Alberto Lastra Universidad de Alcalá Departamento de Física y Matemáticas Ap. de Correos 20, E-28871 Alcalá de Henares Madrid, Spain email: alberto.lastra@uah.es |
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Pascal Remy Laboratoire de Mathematiques de Versailles UVSQ (Paris-Saclay) & CNRS (UMR 8100) 45 avenue des Etats-Unis, 78035 Versailles cedex, France email: pascal.remy@uvsq.fr |
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Maria Suwińska Faculty of Mathematics and Natural Sciences College of Science Cardinal Stefan Wyszynski University in Warsaw Wóycickiego 1/3, 01-938 Warszawa, Poland email: m.suwinska@op.pl |
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