MR2493873 Qing LIU, Nguyen VAN MINH, G. NGUEREKATA and Rong YUAN Qing LIU, Nguyen VAN MINH, G. NGUEREKATA and Rong YUAN Massera Type Theorems for Abstract Functional Differential Equations Funkcialaj Ekvacioj. Serio Internacia 51 2008 329--350 http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-3/51_329.pdf http://www.ams.org/mathscinet-getitem?mr=MR2493873 The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation $\dot u(t)=Au(t)+[{\cal B}u](t)+f(t)$, where $A$ is a closed operator in a Banach space $\mathbb X$, $\cal B$ is a general bounded linear operator in the function space of all $\mathbb X$-valued bounded and uniformly continuous functions that satisfies a so-called autonomous condition. We develop a general procedure to carry out the decomposition that does not need the well-posedness of the equations. The obtained conditions are of Massera type, which are stated in terms of spectral conditions of the operator ${\cal A}+{\cal B}$ and the spectrum of $f$. Moreover, we give conditions for the equation not to have quasi-periodic solutions with different structures of spectrum. The obtained results extend previous ones. Almost periodic solution, Abstract functional differential equation, Massera type theorem, Quasi-periodic solution, Non-existence. 47D06, 34C27. 51-329 2008 Massera Type Theorems for Abstract Functional Differential Equations Qing LIU, Nguyen VAN MINH, G. NGUEREKATA and Rong YUAN Qing LIU, Nguyen VAN MINH, G. NGUEREKATA and Rong YUAN
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