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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A spectral countability condition for almost automorphy of solutions of differential equations
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by Nguyen Van Minh, Toshiki Naito and Gaston Nguerekata PDF
Proc. Amer. Math. Soc. 134 (2006), 3257-3266 Request permission

Abstract:

We consider the almost automorphy of bounded mild solutions to equations of the form \begin{equation*} (*)\quad \qquad \qquad \qquad \qquad \qquad dx/dt = A(t)x + f(t) \quad \qquad \qquad \qquad \qquad \qquad \qquad \end{equation*} with (generally unbounded) $\tau$-periodic $A(\cdot )$ and almost automorphic $f(\cdot )$ in a Banach space $\mathbb {X}$. Under the assumption that $\mathbb {X}$ does not contain $c_0$, the part of the spectrum of the monodromy operator associated with the evolutionary process generated by $A(\cdot )$ on the unit circle is countable. We prove that every bounded mild solution of $(*)$ on the real line is almost automorphic.
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Additional Information
  • Nguyen Van Minh
  • Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
  • Email: vnguyen@westga.edu
  • Toshiki Naito
  • Affiliation: Department of Mathematics, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
  • Email: naito@e-one.uec.ac.jp
  • Gaston Nguerekata
  • Affiliation: Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, Maryland 21251
  • ORCID: 0000-0001-5765-7175
  • Email: gnguerek@jewel.morgan.edu
  • Received by editor(s): May 18, 2005
  • Published electronically: May 12, 2006
  • Communicated by: Carmen C. Chicone
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3257-3266
  • MSC (2000): Primary 47D06; Secondary 34G10, 45M05
  • DOI: https://doi.org/10.1090/S0002-9939-06-08528-5
  • MathSciNet review: 2231910