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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 \(f\)”.

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
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