Geodesic
Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour
Electronic journal of differential equations, Tome 2003 (2003)
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.
Classification : 47D06, 47A55, 34D05, 34G10
Keywords: non-autonomous retarded differential equations, variation of constants formula, dyson-phillips series, asymptotic almost periodicity 
@article{EJDE_2003__2003__a133,
     author = {Boulite,  Said and Maniar,  Lahcen and Moussi,  Mohammed},
     title = {Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1060.47044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a133/}
}
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Boulite,  Said; Maniar,  Lahcen; Moussi,  Mohammed. Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a133/