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

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  • Alberto Lastra
  • Stéphane Malek

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.

Suggested Citation

  • Alberto Lastra & Stéphane Malek, 2012. "On q‐Gevrey Asymptotics for Singularly Perturbed q‐Difference‐Differential Problems with an Irregular Singularity," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:860716
    DOI: 10.1155/2012/860716
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    References listed on IDEAS

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    1. Raghavan Narasimhan & Yves Nievergelt, 2001. "Complex Analysis in One Variable," Springer Books, Springer, edition 0, number 978-1-4612-0175-5, March.
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