Gevrey type solutions of nonlinear difference equations

Abstract

We prove the existence of Gevrey type solutions for locally analytic, nonlinear difference equations possessing a formal solution that belongs to some (generalized) Gevrey class of divergent power series in z^−1/p. We consider different types of domains: domains bounded by a curve with limiting directions −π/2 and π/2 (mod  π), and domains bounded by curves with the same limiting direction, viz. π/2 (mod  π), containing an unbounded part of the imaginary axis.