Stephane MALEK
On singularly perturbed q-difference-differential equations with irregular singularity
(448K, postscript)

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.