 1211 A. Lastra, S. Malek, J. Sanz
 On qasymptotics for linear qdifferencedifferential equations with Fuchsian and irregular singularities
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Jan 31, 12

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Abstract. We consider a Cauchy problem for some family of linear qdifference differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables for given formal power series initial conditions. Under suitable conditions and by the application of certain qBorel and Laplace transforms, we are able to deal with the small divisors phenomenon caused by the Fuchsian singularity, and to construct actual holomorphic solutions of the Cauchy problem whose qasymptotic expansion is the latter formal series. The small divisors's effect is an increase in the order of qexponential growth and the appearance of a power of the factorial in the corresponding qGevrey bounds in the asymptotics.\medskip
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