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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
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