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Some remarks on almost automorphic solutions of some abstract differential equations. (English) Zbl 1040.34068
Summary: We are concerned with both almost automorphic and almost periodic solutions of the differential equation given by $u'(t)= Au(t)+ f(t).$ The cases where $$A$$ is of the simplest type, nilpotent, maximal monotone, or normal, respectively, are considered. In particular, we establish a connection between almost automorphic functions, provided by both the semigroup $$S(t)$$ generated by $$A$$ and the semigroup $$S_\lambda(t)$$ generated by Yosida’s approximation $$A_\lambda$$ of $$A$$.

##### MSC:
 34G10 Linear differential equations in abstract spaces 47D06 One-parameter semigroups and linear evolution equations