On singularly perturbed q -difference-differential equations with irregular singularity

Author： Malek S.  

Publisher： Springer Publishing Company

ISSN： 1079-2724

Source： Journal of Dynamical and Control Systems, Vol.17, Iss.2, 2011-04, pp. : 243-271

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Abstract

We study a q-analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain. We construct solutions of this problem that are holomorphic on open half-q-spirals. Using a version of a q-analog of the Malgrange-Sibuya theorem obtained by J.-P. Ramis, J. Sauloy, and C. Zhang, we show the existence of a formal power-series solution in the perturbation parameter which is the q-asymptotic expansion of these holomorphic solutions.

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