A. LASTRA, S. MALEK
On q-Gevrey asymptotics for singularly perturbed q-difference-differential
problems with an irregular singularity
(380K, pdf)
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 the second author. 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.