Tohoku Mathematical Journal
2006
June
SECOND SERIES VOL. 58, NO. 2

Tohoku Math. J.
58 (2006), 237-258

Title BOREL SUMMABILITY OF DIVERGENT SOLUTIONS FOR SINGULARLY PERTURBED FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

Author Masaki Hibino

(Received May 26, 2004, revised March 8, 2005)
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.

2000 Mathematics Subject Classification. Primary 35C20; Secondary 35C10, 35C15.
Key words and phrases. Singular perturbation, divergent solution, Borel summability, analytic continuation.

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