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...
| Autores: | , |
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| 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 |
| 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. |
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