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

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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.

Keywords

Evolution equation , mild solution , almost automorphy , uniform spectrum
  • 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.
  • Pages: 61–74
  • Date Published: 2008-07-01
  • Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal

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Published

2008-07-01

How to Cite

[1]
K. Ezzinbi, V. Nelson, and G. N‘Gu´er´ekata, “𝐶⁽ⁿ⁾-Almost Automorphic Solutions of Some Nonautonomous Differential Equations”, CUBO, vol. 10, no. 2, pp. 61–74, Jul. 2008.

Issue

Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal

Section

Articles