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January, 2004 Massera's theorem for almost periodic solutions of functional differential equations
Satoru MURAKAMI, Toshiki NAITO, Nguyen Van MINH
J. Math. Soc. Japan 56(1): 247-268 (January, 2004). DOI: 10.2969/jmsj/1191418705


The Massera Theorem for almost periodic solutions of linear periodic ordinary differential equations of the form (*)x=A(t)x+f(t), where f is almost periodic, is stated and proved. Furthermore, it is extended to abstract functional differential equations (**)x=Ax+F(t)xt+f(t), where A is the generator of a compact semigroup, F is periodic and f is almost periodic. The main techniques used in the proofs involve a new variation of constants formula in the phase space and a decomposition theorem for almost periodic solutions.


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Satoru MURAKAMI. Toshiki NAITO. Nguyen Van MINH. "Massera's theorem for almost periodic solutions of functional differential equations." J. Math. Soc. Japan 56 (1) 247 - 268, January, 2004.


Published: January, 2004
First available in Project Euclid: 3 October 2007

zbMATH: 1070.34093
MathSciNet: MR2027625
Digital Object Identifier: 10.2969/jmsj/1191418705

Primary: 34K14
Secondary: 34C27 , 34G10 , 34K30

Keywords: Abstract functional differential equation , almost periodic solutions , Decomposition , Massera's theorem , variation of constants formula

Rights: Copyright © 2004 Mathematical Society of Japan


Vol.56 • No. 1 • January, 2004
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