Geodesic
Almost automorphic solutions of neutral functional differential equations
Electronic Journal of Differential Equations, Tome 2010 (2010).

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

Summary: In this article, we prove the existence and uniqueness of almost automorphic solutions to the non-autonomous evolution equation $$ \frac{d}{dt}(u(t)-F_1(t,B_1u(t)))=A(t)(u(t)-F_1(t,Bu(t)))+F_2(t,u(t),B_2u(t)), \quad t\in \mathbb{R} $$ where $A(t)$ generates a hyperbolic evolution family $U(t,s)$ (not necessarily periodic) in a Banach space, and $B_1,B_2$ are bounded linear operators. The results are obtained by means of fixed point methods.
Classification : 34K05, 34A12, 34A40
Keywords: neutral differential equation, almost automorphic functions, almost periodic functions, exponentially stable semigroup, semigroup of linear operators 
@article{EJDE_2010__2010__a11,
     author = {Mophou, Gis\`ele M. and N'Gu\'er\'ekata, Gaston M.},
     title = {Almost automorphic solutions of neutral functional differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a11/}
}
TY  - JOUR
AU  - Mophou, Gisèle M.
AU  - N'Guérékata, Gaston M.
TI  - Almost automorphic solutions of neutral functional differential equations
JO  - Electronic Journal of Differential Equations
PY  - 2010
VL  - 2010
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a11/
LA  - en
ID  - EJDE_2010__2010__a11
ER  - 
%0 Journal Article
%A Mophou, Gisèle M.
%A N'Guérékata, Gaston M.
%T Almost automorphic solutions of neutral functional differential equations
%J Electronic Journal of Differential Equations
%D 2010
%V 2010
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a11/
%G en
%F EJDE_2010__2010__a11
Mophou, Gisèle M.; N'Guérékata, Gaston M. Almost automorphic solutions of neutral functional differential equations. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a11/