Geodesic
Almost automorphic solutions of neutral functional differential equations
Electronic journal of differential equations, Tome 2010 (2010)
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},
     year = {2010},
     volume = {2010},
     zbl = {1202.34139},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a11/}
}
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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/