ð¶â½â¿â¾-Almost Automorphic Solutions of Some Nonautonomous Differential Equations

Khalil Ezzinbi; Valerie Nelson; Gaston N‘Gu´er´ekata

Authors

Khalil Ezzinbi Universit´e Cadi Ayyad, Facult´e des Sciences Semlalia, D´epartement de Math´ematiques, BP. 2390, Marrakech, Morocco.
Valerie Nelson Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA.
Gaston N‘Gu´er´ekata Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA.

Keywords:

Evolution equation, mild solution, almost automorphy, uniform spectrum

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 âˆˆ â„ and A(t) is Ï„ periodic and the equation x”²(t) = Ax(t) + f(t), t âˆˆ â„ where the operator A generates a quasi-compact semigroup in a Banach space, and in both cases f is C⁽ⁿ⁾-almost automorphic.