Geodesic
Periodicity of mild solutions to higher order differential equations in Banach spaces
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34G10, 34K06, 47D06
Keywords: abstract Cauchy problems, Fourier series, periodic mild solutions, semigroups and cosine families 
@article{EJDE_2004__2004__a84,
     author = {Nguyen, Thanh Lan},
     title = {Periodicity of mild solutions to higher order differential equations in {Banach} spaces},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a84/}
}
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Nguyen, Thanh Lan. Periodicity of mild solutions to higher order differential equations in Banach spaces. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a84/