Journal of the Mathematical Society of Japan

Massera's theorem for almost periodic solutions of functional differential equations

Satoru MURAKAMI, Toshiki NAITO, and Nguyen Van MINH

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 56, Number 1 (2004), 247-268.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418705

Digital Object Identifier
doi:10.2969/jmsj/1191418705

Mathematical Reviews number (MathSciNet)
MR2027625

Zentralblatt MATH identifier
1070.34093

Subjects
Primary: 34K14: Almost and pseudo-periodic solutions
Secondary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 34G10: Linear equations [See also 47D06, 47D09] 34C27: Almost and pseudo-almost periodic solutions

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

Citation

MURAKAMI, Satoru; NAITO, Toshiki; Van MINH, Nguyen. Massera's theorem for almost periodic solutions of functional differential equations. J. Math. Soc. Japan 56 (2004), no. 1, 247--268. doi:10.2969/jmsj/1191418705. https://projecteuclid.org/euclid.jmsj/1191418705


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