On q‐Gevrey Asymptotics for Singularly Perturbed q‐Difference‐Differential Problems with an Irregular Singularity | Zendy

Alberto Lastra | Zendy; Stéphane Malek | Zendy

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On q‐Gevrey Asymptotics for Singularly Perturbed q‐Difference‐Differential Problems with an Irregular Singularity

Author(s) -

Alberto Lastra,

Stéphane Malek

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/860716

Subject(s) - mathematics , singularity , mathematical analysis , differential (mechanical device) , pure mathematics , engineering , aerospace engineering

We study a q-analog of a singularly perturbed Cauchy problem with irregular singularityin 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

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