Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type. I (Q1424089)

This paper deals with the existence of Gevrey asymptotic solutions for the divergent formal solution of a singular first-order linear partial differential equation of nilpotent type with holomorphic coefficients at the origin in \(\mathbb{R}^2\). At first the author proves the existence of asymptotic solutions in a small sector unconditionally. Assuming global analytic continuation properties for the coefficients of the corresponding equation it is shown that the formal solution is Borel summable in appropriate domain and its Borel sum is a holomorphic solution of the equation under consideration.