 1730 Thomas Dreyfus, Alberto Lastra, Stephane Malek
 Twofold qGevrey asymptotics for linear singularly perturbed qdifferencedifferential equations with polynomial coefficients
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Mar 30, 17

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Abstract. We construct analytic and formal solutions for a family of qdifferencedifferential problems,
under the action of a perturbation parameter. This work is a continuation of a prior study focusing on a singularly perturbed qdifferencedifferential problem for which a phenomenon of multilevel qGevrey asymptotics has been observed, owing to the fact that the main equation is factorized as a product of two simpler equations in socalled normal forms, each producing one single level of qGevrey asymptotics. The problem under study in this paper is a priori not factorizable. We follow instead a direct approach developed in a work of the first author based on successive applications of two qBorelLaplace transforms of different orders both to the same initial problem and which can be described by means of a Newton polygon.
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