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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Almost automorphic solutions of evolution equations
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by Toka Diagana, Gaston Nguerekata and Nguyen Van Minh PDF
Proc. Amer. Math. Soc. 132 (2004), 3289-3298 Request permission

Abstract:

This paper is concerned with the existence of almost automorphic mild solutions to equations of the form \[ \dot u(t)= Au(t)+f(t),\tag *{$(*)$}\] where $A$ generates a holomorphic semigroup and $f$ is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to $(*)$ in terms of the imaginary spectrum of $A$ and the uniform spectrum of $f$.
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Additional Information
  • Toka Diagana
  • Affiliation: Department of Mathematics, Howard University, 2441 6th Street N.W., Washington D.C. 20059
  • MR Author ID: 662718
  • Email: tdiagana@howard.edu
  • 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
  • Nguyen Van Minh
  • Affiliation: Department of Mathematics, Hanoi University of Science, Khoa Toan, Dai Hoc Khoa Hoc Tu Nhien, 334 Nguyen Trai, Hanoi, Vietnam
  • Address at time of publication: Department of Mathematics, State University of West Georgia, Carrollton, Georgia 30118
  • Email: nvminh@netnam.vn, ngvminh@yahoo.com
  • Received by editor(s): July 16, 2003
  • Published electronically: June 18, 2004
  • Communicated by: Carmen C. Chicone
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 3289-3298
  • MSC (2000): Primary 34G10; Secondary 43A60
  • DOI: https://doi.org/10.1090/S0002-9939-04-07571-9
  • MathSciNet review: 2073304