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

Alberto Lastra and Stéphane Malek

Abstract and Applied Analysis, 2012, vol. 2012, 1-35

Abstract:

We study a -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 -spirals to the origin. By means of a -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 -Gevrey asymptotic expansion (of certain type) of the actual solutions.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:860716

DOI: 10.1155/2012/860716

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