Abstract

Here, the existence of periodic solutions for the evolution equation \[ 0 \in \frac {du}{dt} + A(t)u \] is studied, where \(u\) lies in a Banach space and \(A(t)\) is an almost-periodic and possibly nonlinear multivalued operator. The authors give a condition which guarantees that all generalized solutions to the above equation approach a uniquely determined almost-periodic solution. This theorem extends some recent results by S. Kato, N.V. Medvedev, G. Seifert, and O. Arino.