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Pseudo-almost-periodic solutions for some differential equations in a Banach space. (English) Zbl 0874.34041

Differential equations of the form

dx/dt=ft , x ( t )

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 (1/2T) -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.

MSC:
34C27Almost and pseudo-almost periodic solutions of ODE
34G20Nonlinear ODE in abstract spaces