On q-Gevrey Asymptotics for Singularly Perturbed q-Difference-Differential Problems with an Irregular Singularity. (6th February 2012) - Lastra, Alberto; Malek, Stéphane
Abstract : We study a q -analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain which generalizes a previous result by Malek in (2011). First, we construct solutions defined in open q -spirals to the origin. By means of a q -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 q -Gevrey asymptotic expansion (of certain type) of the actual solutions.