On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
Identificadores
Enlace permanente (URI): http://hdl.handle.net/10017/41470DOI: 10.1016/j.jde.2012.01.038
ISSN: 0022-0396
Editor
Elsevier
Fecha de publicación
2012-05-15Cita bibliográfica
Lastra, A., Malek, S. & Sanz, J. 2012, “On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities”, Journal of Differential Equations, vol. 252, no. 10, pp. 5185-5216
Palabras clave
q-Difference-differential equations
q-Laplace transform
Formal power series solutions
q-Gevrey asymptotic expansions
Small divisors
Fuchsian and irregular singularities
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/acceptedVersion
Versión del editor
https://doi.org/10.1016/j.jde.2012.01.038Derechos
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2012 Elsevier
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
We consider a Cauchy problem for some family of linear q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables X (t, z) for given formal power series initial conditions. Under suitable conditions and by the application of certain q-Borel and Laplace transforms (introduced by J.-P. Ramis and C. Zhang), 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 q-asymptotic expansion in t, uniformly for z in the compact sets of , is X (t, z) . The small divisorsʼ effect is an increase in the order of q-exponential growth and the appearance of a power of the factorial in the corresponding q-Gevrey bounds in the asymptotics.
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- MATEMATIC - Artículos [172]