Geodesic
Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a33,
     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},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a33/}
}
TY  - JOUR
AU  - Boulite, Said
AU  - Maniar, Lahcen
AU  - Moussi, Mohammed
TI  - Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour
JO  - Electronic Journal of Differential Equations
PY  - 2003
VL  - 2003
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a33/
LA  - en
ID  - EJDE_2003__2003__a33
ER  - 
%0 Journal Article
%A Boulite, Said
%A Maniar, Lahcen
%A Moussi, Mohammed
%T Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour
%J Electronic Journal of Differential Equations
%D 2003
%V 2003
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a33/
%G en
%F EJDE_2003__2003__a33
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__a33/