On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations

A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic te...

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Detalles Bibliográficos
Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Malek, Stephane
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/60267
Acceso en línea:http://hdl.handle.net/10017/60267
https://dx.doi.org/10.1007/s00208-023-02780-x
Access Level:acceso abierto
Palabra clave:q-Gevrey asymptotic expansions
Monodromy
logarithmic type solutions
Singularly perturbed
Formal solution
Matemáticas
Mathematics
Descripción
Sumario:A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-Gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.