Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour
Date
2003-05-29
Authors
Boulite, Said
Maniar, Lahcen
Moussi, Mohammed
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
This paper is devoted to show a variation of constants formula for the operator solution to the non-autonomous retarded differential equation
x'(t) = A(t)x(t) + L(t)xt + ƒ(t), xs = φ, t ≥ s ≥ 0,
in terms of the inhomogeneous term ƒ, which will allow us to study the asymptotic behaviour of this solution. We treat also the existence of fundamental solutions and the stability of semi-linear retarded differential equations.
Description
Keywords
Non-autonomous retarded differential equations, Variation of constants formula, Dyson-Phillips series, Asymptotic almost periodicity
Citation
Boulite, S., Maniar, L., & Moussi, M. (2003). Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour. <i>Electronic Journal of Differential Equations, 2003</i>(62), pp. 1-15.
Rights
Attribution 4.0 International