𝐶⁽ⁿ⁾-Almost Automorphic Solutions of Some Nonautonomous Differential Equations
Author
Ezzinbi, Khalil
Nelson, Valerie
N’Gu´er´ekata, Gaston
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 ℂk: x′(t) = A(t)x(t)+f(t), t ∈ ℝ and A(t) is τ periodic and the equation x′(t) = Ax(t) + f(t), t ∈ ℝ where the operator A generates a quasi-compact semigroup in a Banach space, and in both cases f is C(n)-almost automorphic.