On Stepanov-like (pseudo) almost automorphic functions. (English) Zbl 1229.34092
A new composition theorem for Stepanov-like pseudo almost automorphic functions is presented in this nice paper. Then, it is used to obtain the existence and uniqueness of pseudo almost automorphic solutions to the semilinear differential equation
\[ u'(t)=Au(t)+F(t,u(t)), \]
where the operator \(A\) generates an exponentially stable \(C_0\)-semigroup of operators \((T(t))_{t\geq 0}\). The latter generalizes a recent result by T. Diagana.
\[ u'(t)=Au(t)+F(t,u(t)), \]
where the operator \(A\) generates an exponentially stable \(C_0\)-semigroup of operators \((T(t))_{t\geq 0}\). The latter generalizes a recent result by T. Diagana.
Reviewer: Gaston M. N’Guerekata (Baltimore)
MSC:
| 34G10 | Linear differential equations in abstract spaces |
| 43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
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