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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
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