Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations. (English) Zbl 0987.34062

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.


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
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