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.