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Asymptotic Behavior of Linear Almost Periodic Differential Equations

  • Bui Xuan Dieu
  • Luu Hoang Duc
  • Stefan Siegmund
  • Nguyen Van Minh
Conference paper
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 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Bui Xuan Dieu
    • 1
    • 2
  • Luu Hoang Duc
    • 1
    • 3
  • Stefan Siegmund
    • 1
  • Nguyen Van Minh
    • 4
    • 5
  1. 1.Department of MathematicsDresden University of TechnologyDresdenGermany
  2. 2.School of Applied Mathematics & Informatics, Hanoi University of Science and TechnologyHa NoiViet Nam
  3. 3.Institute of MathematicsVietnam Academy of Science and TechnologyHa NoiViet Nam
  4. 4.Department of MathematicsColumbus State UniversityColumbusUSA
  5. 5.Department of Mathematics & StatisticsUniversity of Arkansas at Little RockLittle RockUSA

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