Tohoku Mathematical Journal

Borel summability of divergent solutions for singularly perturbed first-order ordinary differential equations

Masaki Hibino

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Abstract

This paper is concerned with the study of the Borel summability of divergent solutions for singularly perturbed inhomogeneous first-order linear ordinary differential equations which have a regularity at the origin. In order to assure the Borel summability of divergent solutions, global analytic continuation properties for coefficients are required despite the fact that the domain of the Borel sum is local.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 2 (2006), 237-258.

Dates
First available in Project Euclid: 22 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1156256403

Digital Object Identifier
doi:10.2748/tmj/1156256403

Mathematical Reviews number (MathSciNet)
MR2248432

Zentralblatt MATH identifier
1118.34083

Subjects
Primary: 35C20: Asymptotic expansions
Secondary: 35C10: Series solutions 35C15: Integral representations of solutions

Keywords
Singular perturbation divergent solution Borel summability analytic continuation

Citation

Hibino, Masaki. Borel summability of divergent solutions for singularly perturbed first-order ordinary differential equations. Tohoku Math. J. (2) 58 (2006), no. 2, 237--258. doi:10.2748/tmj/1156256403. https://projecteuclid.org/euclid.tmj/1156256403


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