## Journal of the Mathematical Society of Japan

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

#### Abstract

The Massera Theorem for almost periodic solutions of linear periodic ordinary differential equations of the form $(*)x^{\prime}=A(t)x+f(t)$, where $f$ is almost periodic, is stated and proved. Furthermore, it is extended to abstract functional differential equations $(**)x^{\prime}=Ax+F(t)x_{t}+f(t)$, 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

https://projecteuclid.org/euclid.jmsj/1191418705

Digital Object Identifier
doi:10.2969/jmsj/1191418705

Mathematical Reviews number (MathSciNet)
MR2027625

Zentralblatt MATH identifier
1070.34093

#### 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