## Differential and Integral Equations

### Almost periodicity and stability for solutions to functional-differential equations with infinite delay

#### Abstract

We develop results on (a) almost periodicity properties and (b) (exponential) asymptotic stability of solutions to the functional differential equations with infinite delay (FDE) $\dot{x}(t) + \alpha x(t) + Bx(t) \ni F(x_t) ,$ $t \geq 0,$ $x |_{\mathbb{R}^-} = \varphi \in E$ in a context which allows for a (generally) nonlinear and multivalued accretive state-responsive operator $B \subset X \times X$ in a Banach state space $X$ and a locally defined and locally Lipschitz continuous history-responsive function $F : D(F) \subset E \to X,$ in an appropriate initial history space $E$ of continuous functions from $\mathbb{R}^-$ into $X.$ Applications to models from population dynamics (delay logistic equation) and biology (Goodwin oscillator) are presented.

#### Article information

Source
Differential Integral Equations, Volume 9, Number 6 (1996), 1225-1252.

Dates
First available in Project Euclid: 6 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367846898

Mathematical Reviews number (MathSciNet)
MR1409925

Zentralblatt MATH identifier
0879.34073

#### Citation

Ruess, Wolfgang M.; Summers, William H. Almost periodicity and stability for solutions to functional-differential equations with infinite delay. Differential Integral Equations 9 (1996), no. 6, 1225--1252. https://projecteuclid.org/euclid.die/1367846898