Parametric Borel summability of semilinear partial differential equation (Microlocal Analysis and Singular Perturbation Theory)

Abstract

In [1], Balser and Kostov studied the parametric Borel summability for a system of ordinary differential equations of Fuchsian type. They noted that a certain Diophantine phenomenon enters in the summability. In fact, they showed, by a counter example, that a Diophantine condition is necessary in general for the parametric Borel summability. In this paper we shall show the parametric Borel summability for a first order semilinear partial differential equation as well as an ordinary differential equation which does not necessarily satisfy Balser-Kostov's Diophantine-type condition.