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Asymptotically almost periodic solutions of evolution equations in Banach spaces. (English) Zbl 0837.34067
From the authors’ introduction: “In this paper, we study the asymptotic behavior of solutions to the differential equation $$u'(t) = Au(t) + f(t)$$, $$t \in \mathbb{R}$$, where $$A$$ is the generator of a $$C_0$$-semigroup of operators in a Banach space $$E$$, and $$f$$ is a given $$E$$-valued function on $$\mathbb{R}$$. Our main objective is to deduce almost periodicity and related properties of the solution $$u$$ from corresponding properties of the inhomogeneous part $$f$$”.

##### MSC:
 34G20 Nonlinear differential equations in abstract spaces 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 47H20 Semigroups of nonlinear operators 47D06 One-parameter semigroups and linear evolution equations
##### Keywords:
asymptotic behavior; almost periodicity
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