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

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.


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