Asymptotically almost periodic solutions of evolution equations in Banach spaces. (English) Zbl 0837.34067

Ruess, Wolfgang M.; Vũ Quôc Phóng

J. Differ. Equations 122, No. 2, 282-301 (1995).

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 \(f\)”.

Reviewer: S.Zaidman (Montréal)

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