# zbMATH — the first resource for mathematics

Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations. (English) Zbl 1077.47058
The paper studies the existence of unique almost automorphic solutions to the equations $x'(t)=Ax(t)+f(t),\;x'(t)=Ax(t)+g \bigl(t,x(t)\bigr),\quad t\in\mathbb{R},\tag{1}$ 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 $$t\in\mathbb{R}$$ for each $$x\in X$$.

##### MSC:
 47N20 Applications of operator theory to differential and integral equations 34G10 Linear differential equations in abstract spaces 47D06 One-parameter semigroups and linear evolution equations
Full Text: