## Almost periodicity and stability for solutions to functional differential equations with infinite delay.(English)Zbl 0879.34073

The subject of the paper is almost periodicity and stability of solutions to a Banach space valued functional differential equation with infinite delay. While the linear part of the equation is a multivalued accretive operator, the nonlinear part with delay is assumed to be Lipschitz continuous. Under local conditions the semigroup method is applied to derive almost periodicity properties and stability results for solutions of the equation in question. The general results are then applied to the delay logistic equation from population dynamics and the Goodwin oscillator with infinite delay as a model for biochemical reaction sequences.

### MSC:

 34K30 Functional-differential equations in abstract spaces 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations