On Gevrey asymptotics for singularly perturbed difference-differential problems with an irregular singularity
arXiv:1106.0401
Abstract
We study a analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain which generalizes a previous result by S. Malek in \cite{malek}. First, we construct solutions defined in open spirals to the origin. By means of a Gevrey version of Malgrange-Sibuya theorem we show the existence of a formal power series in the perturbation parameter which turns out to be the Gevrey asymptotic expansion (of certain type) of the actual solutions.
arXiv comment30 pages