Massera’s theorem for almost periodic solutions of functional differential equations. (English) Zbl 1070.34093

Murakami, Satoru; Naito, Toshiki; Van Minh, Nguyen

J. Math. Soc. Japan 56, No. 1, 247-268 (2004).

The authors establish an existence theorem of Massera type for almost-periodic solutions of linear periodic ordinary differential equations of the form \(x'=A(t)x+f(t)\), where \(A(t)\) is a continuous matrix function which is periodic in \(t\), and \(f\) is almost-periodic. Furthermore, they extend their result to abstract functional-differential equations \(x'=Ax+f(t)x_t+f(t)\), where \(A\) is the generator of a compact semigroup, \(F\) is periodic and \(f\) is almost periodic. The main techniques used in this paper involve a new variation of constants formula in the phase space and a decomposition theorem for almost-periodic solutions.

Reviewer: Meng Fan (Changchun)

MSC:

34K14	Almost and pseudo-almost periodic solutions to functional-differential equations
34K30	Functional-differential equations in abstract spaces

Keywords:

almost-periodic solutions; Massera’s theorem