Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 79, pp. 1-12.

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

Author: Thanh Lan Nguyen (Western Kentucky Univ., Bowling Green, KY, USA)
 
Abstract:
 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.