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Zbl 0874.34041
Ait, Dads E.; Ezzinbi, K.; Arino, O.
Pseudo-almost-periodic solutions for some differential equations in a Banach space.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 28, No.7, 1141-1155 (1997). ISSN 0362-546X

Differential equations of the form $$dx/dt =f\bigl(t,x(t) \bigr)$$ are considered. A very important question in many practical situations connected with this type of equation is to know if there exists a mean value of a bounded solution $x(t)$. By the mean value it is understood the limit $$\lim_{T\to\infty} (1/2T) \int^T_{-T} x(t)dt$$ if it exists. A generalization of the problem with values of pseudo-almost-periodic functions in a Banach space is proposed.
[S.G.Zhuravlev (Moskva)]
MSC 2000:
*34C27 Almost periodic solutions of ODE
34G20 Nonlinear ODE in abstract spaces

Keywords: almost periodic functions; pseudo-almost-periodic functions; asymptotic almost-periodic functions

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