On $q-$Gevrey asymptotics for singularly perturbed $q-$difference-differential problems with an irregular singularity
Analysis of PDEs
2011-11-30 v2
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.
Keywords
Cite
@article{arxiv.1106.0401,
title = {On $q-$Gevrey asymptotics for singularly perturbed $q-$difference-differential problems with an irregular singularity},
author = {Alberto Lastra and Stéphane Malek},
journal= {arXiv preprint arXiv:1106.0401},
year = {2011}
}
Comments
30 pages