Gühring, Gabriele; Räbiger, Frank Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations. (English) Zbl 0987.34062 Abstr. Appl. Anal. 4, No. 3, 169-194 (1999). The authors study the nonautonomous Cauchy problem \[ \dot u(t) =Au(t)+ B(t)u(t)+ f(t),\;t\in \mathbb{R}, \] for a Hille-Yosida operator \(A\) and relatively bounded operators \(B(t)\). They prove qualitative properties of the solution \(u(\cdot)\) such as periodicity or almost-periodicity. The main applications are made to nonautonomous delay differential equations. Reviewer: Rainer Nagel (Tübingen) Cited in 1 ReviewCited in 21 Documents MSC: 34G10 Linear differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations 47D06 One-parameter semigroups and linear evolution equations 47H14 Perturbations of nonlinear operators 34K05 General theory of functional-differential equations Keywords:asymptotic properties; mild solutions; nonautonomous evolution equations; retarded differential equations; periodicity; almost-periodicity PDFBibTeX XMLCite \textit{G. Gühring} and \textit{F. Räbiger}, Abstr. Appl. Anal. 4, No. 3, 169--194 (1999; Zbl 0987.34062) Full Text: DOI EuDML Link