Electron. J. Diff. Eqns., Vol. 2004(2004), No. 79, pp. 1-12.

Periodicity of mild solutions to higher order differential equations in Banach spaces

Thanh Lan Nguyen

We give necessary and sufficient conditions for the periodicity of mild solutions to the the higher order differential equation $u^{(n)}(t)=Au(t)+f(t)$, $0\le t \le T$, in a Banach space $E$. Applications are made to the cases, when $A$ generates a $C_0$-semigroup or a cosine family, and when $E$ is a Hilbert space.

Submitted February 18, 2004. Published June 4, 2004.
Math Subject Classifications: 34G10, 34K06, 47D06.
Key Words: Abstract Cauchy problems, Fourier series, periodic mild solutions, semigroups and cosine families.

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Thanh Lan Nguyen
Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101, USA
email: Lan.Nguyen@wku.edu

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