Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 62, pp. 1-15.
Title: Non-autonomous retarded differential equations:
the variation of constants formulas and the asymptotic behaviour
Authors: Said Boulite (Univ. Cadi Ayyad, Morocco)
Lahcen Maniar (Univ. Cadi Ayyad, Morocco)
Mohammed Moussi (Univ. Mohammed I, Morocco)
Abstract:
This paper is devoted to show a variation of constants formula for the
operator solution to the non-autonomous retarded differential equation
$$
x'(t)=A(t)x(t)+L(t)x_t+f(t),\quad x_s=\varphi, \quad t\geq s\geq 0,
$$
in terms of the inhomogeneous term $f$, 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.
Submitted November 4, 2002. Published May 29, 2003.
Math Subject Classifications: 47D06, 47A55, 34D05, 34G10.
Key Words: Non-autonomous retarded differential equations;
variation of constants formula; Dyson-Phillips series;
asymptotic almost periodicity.