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1996 Almost periodicity and stability for solutions to functional-differential equations with infinite delay
Wolfgang M. Ruess, William H. Summers
Differential Integral Equations 9(6): 1225-1252 (1996).

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.

Citation

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Wolfgang M. Ruess. William H. Summers. "Almost periodicity and stability for solutions to functional-differential equations with infinite delay." Differential Integral Equations 9 (6) 1225 - 1252, 1996.

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0879.34073
MathSciNet: MR1409925

Subjects:
Primary: 34K30

Rights: Copyright © 1996 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.9 • No. 6 • 1996
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