On parametric multilevel q -Gevrey asymptotics for some linear q -difference-differential equations

Advances in Difference Equations

Alberto Lastra⁵  Stphane Malek⁷ 

[1] de Henares, Spain;, Alcalá, University of Lille 1, Villeneuve d’Ascq Cedex, France;Departamento de FíLaboratoire Paul Painlevésica y Matemáticas, University of Alcalá

关键词: asymptotic expansion;    Borel-Laplace transform;    Fourier transform;    formal power series;    singular perturbation;    q-difference-differential equation;    35C10;    35C20;   

DOI  :  10.1186/s13662-015-0678-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study linear q-difference-differential equations under the action of a perturbation parameter ϵ. This work deals with a q-analog of the research made in (Lastra and Malek in Adv. Differ. Equ. 2015:200, 2015) giving rise to a generalization of the work (Malek in Funkc. Ekvacioj, 2015, to appear). This generalization is related to the nature of the forcing term which suggests the use of a q-analog of an acceleration procedure. The proof leans on a q-analog of the so-called Ramis-Sibuya theorem which entails two distinct q-Gevrey orders. The work concludes with an application of the main result when the forcing term solves a related problem.

【 授权许可】

CC BY