On $C^{\left(n\right)}$-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces

Jean-Bernard Baillon, et al. "On $C^{(n)}$-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces." Commentationes Mathematicae 46.2 (2006): null. <http://eudml.org/doc/291638>.

@article{Jean2006,
abstract = {In this paper we prove the existence and uniqueness of $C^\{(n)\}$-almost periodic solutions to the nonautonomous ordinary differential equation $x^\{\prime \}(t) = A(t)x(t) + f(t)$, $t\in \mathbb \{R\}$, where $A(t)$ generates an exponentially stable family of operators $(U (t, s))$$t\ge s$ and $f$ is a $C^\{(n)\}$-almost periodic function with values in a Banach space $X$. We also study a Volterra-like equation with a $C^\{(n)\}$-almost periodic solution.},
author = {Jean-Bernard Baillon, Joël Blot, Gaston M. N'Guérékata, Denis Pennequin},
journal = {Commentationes Mathematicae},
keywords = {$C^\{(n)\}$-almost periodic function; family of bounded operators; exponentially stable; Acquistapace-Terreni conditions; uniform spectrum of bounded functions},
language = {eng},
number = {2},
pages = {null},
title = {On $C^\{(n)\}$-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces},
url = {http://eudml.org/doc/291638},
volume = {46},
year = {2006},
}

TY - JOUR
AU - Jean-Bernard Baillon
AU - Joël Blot
AU - Gaston M. N'Guérékata
AU - Denis Pennequin
TI - On $C^{(n)}$-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces
JO - Commentationes Mathematicae
PY - 2006
VL - 46
IS - 2
SP - null
AB - In this paper we prove the existence and uniqueness of $C^{(n)}$-almost periodic solutions to the nonautonomous ordinary differential equation $x^{\prime }(t) = A(t)x(t) + f(t)$, $t\in \mathbb {R}$, where $A(t)$ generates an exponentially stable family of operators $(U (t, s))$$t\ge s$ and $f$ is a $C^{(n)}$-almost periodic function with values in a Banach space $X$. We also study a Volterra-like equation with a $C^{(n)}$-almost periodic solution.
LA - eng
KW - $C^{(n)}$-almost periodic function; family of bounded operators; exponentially stable; Acquistapace-Terreni conditions; uniform spectrum of bounded functions
UR - http://eudml.org/doc/291638
ER -