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Zbl 1077.47058
N'Guérékata, Gaston M.
Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations.
(English)
[J] Semigroup Forum 69, No. 1, 80-86 (2004). ISSN 0037-1912

The paper studies the existence of unique almost automorphic solutions to the equations $$x'(t)=Ax(t)+f(t),\ x'(t)=Ax(t)+g \bigl(t,x(t)\bigr),\quad t\in\bbfR,\tag 1$$ when $A$ generates an exponentially $C_0$-semigroup on a Banach space $X$, and the functions $f(t)$ and $g(t,x)$ are almost automorphic in $t\in\bbfR$ for each $x\in X$.
[Lahcen Maniar (Marrakech)]
MSC 2000:
*47N20 Appl. of operator theory to differential and integral equations
34G10 Linear ODE in abstract spaces
47D06 One-parameter semigroups and linear evolution equations

Keywords: semilinear differential equations; exponentially $C_0$-semigroup

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