Gevrey type solutions of nonlinear difference equations

Article type: Research Article

Authors: Immink, G.K.

Affiliations: Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands E-mail: g.k.immink@rug.nl

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.

Journal: Asymptotic Analysis, vol. 50, no. 3-4, pp. 205-237, 2006