Abstract:
A q‐analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain is studied. Our result generalizes a previous result by S. Malek in [1]. First, we construct solutions defined in open q‐spirals to the origin. Afterwards, we obtain the existence of a formal power series in the perturbation parameter which represents the solution and is the q‐Gevrey asymptotic expansion of the actual solutions. This is achieved by means of a q‐Gevrey version of Malgrange‐Sibuya theorem. (Joint work with Stéphane Malek.) [1] S. Malek, Singularly perturbed q‐difference‐differential equations with irregular singularity, J. Dynam. Control. Syst. 17 (2011),no.2.