Levitan/Bohr Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Differential Equations
The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson stable solutions of the second order differential equation (1) x′′ = f( (t, y), x, x′), (y 2 Y ) where Y is a complete metric space and (Y, R, ) is a dynamical system (also call...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/23677 |
| Acesso em linha: | http://hdl.handle.net/11441/23677 https://doi.org/10.1016/j.jde.2011.04.021 |
| Access Level: | acceso abierto |
| Palavra-chave: | Non-autonomous dynamical systems skew-product systems cocycles quasi-periodic Bohr/Levitan almost periodic almost automorphic pseudo-recurrent solutions monotone second order equation |
| Resumo: | The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson stable solutions of the second order differential equation (1) x′′ = f( (t, y), x, x′), (y 2 Y ) where Y is a complete metric space and (Y, R, ) is a dynamical system (also called a driving system). When the function f in (1) is increasing with respect to its second variable, the existence of at least one quasi periodic (respectively, Bohr almost periodic, almost automorphic, recurrent, pseudo recurrent, Levitan almost periodic, almost recurrent, Poisson stable) solution of (1) is proved under the condition that (1) admits at least one solution ' such that ' and '′ are bounded on the real axis. |
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