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Mathematical Sciences with Multidisciplinary Applications pp 113–132Cite as

Asymptotic Behavior of Linear Almost Periodic Differential Equations

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 157)

Abstract

The present paper is concerned with strong stability of solutions of non-autonomous equations of the form \(\dot{u}(t) = A(t)u(t)\), where A(t) is an unbounded operator in a Banach space depending almost periodically on t. A general condition on strong stability is given in terms of Perron conditions on the solvability of the associated inhomogeneous equation.

Keywords

  • Strong stability
  • Non-autonomous equation
  • Almost periodicity
  • Evolution semigroup
  • Perron type conditions

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Acknowledgements

The first author was supported by the Vietnamese Ministry of Education and Training (MOET) Scholarship Scheme (Project 322) and the Graduate Academy (GA) of the TU Dresden (PSPElement: F-00361-553-52A-2330000) in accordance with the funding regulations of the German Research Foundation (DFG). The second author was supported by DFG under grant number Si801/6-1 and NAFOSTED under grant number 101.02-2011.47.

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Authors and Affiliations

  1. Department of Mathematics, Dresden University of Technology, 01062, Dresden, Germany

    Bui Xuan Dieu, Luu Hoang Duc & Stefan Siegmund

  2. School of Applied Mathematics & Informatics, Hanoi University of Science and Technology, 01 Dai Co Viet Road, Ha Noi, Viet Nam

    Bui Xuan Dieu

  3. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307, Ha Noi, Viet Nam

    Luu Hoang Duc

  4. Department of Mathematics, Columbus State University, 4225 University Avenue, Columbus, GA, 31907, USA

    Nguyen Van Minh

  5. Department of Mathematics & Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Nguyen Van Minh

Authors
  1. Bui Xuan Dieu
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  2. Luu Hoang Duc
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  3. Stefan Siegmund
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  4. Nguyen Van Minh
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Corresponding author

Correspondence to Nguyen Van Minh .

Editor information

Editors and Affiliations

  1. Dept of Mathematics and Economics, Virginia State University, Petersburg, Virginia, USA

    Bourama Toni

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Dieu, B.X., Duc, L.H., Siegmund, S., Van Minh, N. (2016). Asymptotic Behavior of Linear Almost Periodic Differential Equations. In: Toni, B. (eds) Mathematical Sciences with Multidisciplinary Applications. Springer Proceedings in Mathematics & Statistics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-31323-8_7

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