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

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  • Alberto Lastra
  • Stéphane Malek

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.

Suggested Citation

  • Alberto Lastra & Stéphane Malek, 2012. "On -Gevrey Asymptotics for Singularly Perturbed -Difference-Differential Problems with an Irregular Singularity," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-35, February.
    • Handle: RePEc:hin:jnlaaa:860716
    DOI: 10.1155/2012/860716
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