10-164 Stephane MALEK

On singularly perturbed q-difference-differential equations with irregular singularity (448K, postscript) Oct 5, 10

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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 which 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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