𝐶⁽ⁿ⁾-Almost Automorphic Solutions of Some Nonautonomous Differential Equations

Abstract

This paper is concerned with the study of properties of C⁽ⁿ⁾-almost automorphic functions and their uniform spectra. We apply the obtained results to prove Massera type theorems for the nonautonomous differential equation in â„‚^k: x”²(t) = A(t)x(t)+f(t), t ∈ â„ and A(t) is Ï„ periodic and the equation x”²(t) = Ax(t) + f(t), t ∈ â„ where the operator A generates a quasi-compact semigroup in a Banach space, and in both cases f is C⁽ⁿ⁾-almost automorphic.