This paper is concerned with the
existence of the Gevrey
asymptotic solutions for the
divergent formal solution of
singular first order linear
partial differential equations of
nilpotent type. By using the
Gevrey version of Borel-Ritt's
theorem, we can prove the
existence of asymptotic solutions in
a small sector unconditionally.
However, when we require the Borel
summability of the formal
solution (that is, the existence
of asymptotic solutions in an
open disk), global analytic
continuation properties for
coefficients are demanded.