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

• Autorzy: Jean-Bernard Baillon , Joël Blot , Gaston M. N'Guérékata , Denis Pennequin
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove the existence and uniqueness of \(C^{(n)}\)-almost periodic solutions to the nonautonomous ordinary differential equation \(x'(t) = A(t)x(t) + f(t)\), \(t\in\mathbb{R}\), where \(A(t)\) generates an exponentially stable family of operators \((U (t, s))\) \(t\geq s\) 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.

Słowa kluczowe

EN

\(C^{(n)}\)-almost periodic function; family of bounded operators; exponentially stable; Acquistapace-Terreni conditions; uniform spectrum of bounded functions

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2006
• Tom: 46
• Numer: 2

Daty

wydano

2006

online

2017-12-19

Twórcy

autor

Jean-Bernard Baillon

autor

Joël Blot

autor

Gaston M. N'Guérékata

autor

Denis Pennequin

Identyfikatory

DOI

10.14708/cm.v46i2.5222