Article
Levitan/Bohr Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Differential Equations
Author/s | Caraballo Garrido, Tomás
Cheban, David |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2007 |
Deposit Date | 2015-04-08 |
Published in |
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Abstract | 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 ) ... 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. |
Citation | Caraballo Garrido, T. y Cheban, D. (2007). Levitan/Bohr Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Differential Equations. Journal of Differential Equations, 19 (1), 177-196. |
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