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

Alberto Lastra and Stéphane Malek

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/860716

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:860716

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