ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34K05, 34K25 Hou, Zhanyuan, and Cassell, J. S., London Guildhall University, England L^{p}-Perturbation of Linear Functional Differential Equations The asymptotic behaviour is studied of a class of linear retarded functional differential equations, x′(t) = L(t, x_{t}) (t ≥ t_{0}). An equation is said to be exponentially dominated if it has a solution x_{0}(t) = exp{∫_{t_{0}}^{t} λ(s)ds} on [t_{0} − r, ∞) and every solution has the asymptotic form x(t) = {c + o(e^{−αt})}x_{0}(t) as t → ∞, where α > 0 is independent of x but c is a constant dependent on x. Classes of equations that are exponentially dominated have been found. Moreover, it is shown that L^{p}-perturbations of equations of these classes, x′(t) = L(t, x_{t}) + L̃(t, x_{t}) with ∫_{t_{0}}^{∞} ∥L̃(t, ·)∥^{p}dt < ∞ (p ≥ 1), are still exponentially dominated on [T, ∞) when T ≥ t_{0} is large enough.