18-7 A. Lastra, S. Malek

On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities (447K, pdf) Jan 24, 18

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Abstract. We study a Cauchy problem for a certain family of q-difference-differential equations. We construct actual holomorphic solutions with the help of a q-analog to the classical Borel/Laplace summation and we study their asymptotic expansions in time variable. These asymptotic expansions are generically divergent due to an irregular singularity involved in the equation. Small divisors phenomena appear owing to the presence of a Fuchsian singularity which causes the appearance of a subexponential Gevrey growth in the asymptotic expansions.

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