On q-Gevrey Asymptotics for Singularly Perturbed q-Difference-Differential Problems with an Irregular Singularity. (6th February 2012)

• Record Type: Journal Article
• Authors: Lastra, Alberto; Malek, Stéphane
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-02-06
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/860716
• Languages: English
• ISSNs: 1085-3375

Abstract

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.