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ANNALES SOCIETATIS MATHEMATICAE POLONAE Series I: COMMENTATIONES MATHEMATICAE ROCZNIKI POLSKIEGO TOWARZYSTWA MATEMATYCZNEGO Seria I: PRACE MATEMATYCZNE XLVI (2) (2006), 263-273 On C (n)-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces

Jean-Bernard Baillon, Joël Blot, Gaston N'guérékata
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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 ∈ R, where A(t) generates an exponentially stable family of operators (U (t, s)) t≥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. 1991 Mathematics Subject Classification: 34C37;43A60;34G20. Key words and phrases: C
more » ... periodic function, family of bounded operators, exponentially stable, Acquistapace-Terreni conditions, uniform spectrum of bounded functions.
fatcat:uigrvavrtjgihbnp3mystnza6q
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Jean-Bernard Baillon, Joël Blot, Gaston N'guérékata. "ANNALES SOCIETATIS MATHEMATICAE POLONAE Series I: COMMENTATIONES MATHEMATICAE ROCZNIKI POLSKIEGO TOWARZYSTWA MATEMATYCZNEGO Seria I: PRACE MATEMATYCZNE XLVI (2) (2006), 263-273 On C (n)-Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces."