%0 Journal Article
%T Periodicity of mild solutions to higher order differential equations in Banach spaces
%A Thanh Lan Nguyen
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X We give necessary and sufficient conditions for the periodicity of mild solutions to the the higher order differential equation $u^{(n)}(t)=Au(t)+f(t)$, $0le t le T$, 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.
%K Abstract Cauchy problems
%K Fourier series
%K periodic mild solutions
%K semigroups and cosine families.
%U http://ejde.math.txstate.edu/Volumes/2004/79/abstr.html