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.
"Borel summability of divergent solutions for singularly perturbed first-order ordinary differential equations." Tohoku Math. J. (2) 58 (2) 237 - 258, 2006. https://doi.org/10.2748/tmj/1156256403