Korean Journal of Mathematics

  • 제28권2호
  • /
  • Pages.223-240
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  • 2020
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ALMOST PERIODIC SOLUTIONS OF PERIODIC SECOND ORDER LINEAR EVOLUTION EQUATIONS

  • Nguyen, Huu Tri (Division of Mathematics, Truong THPT Trung Van Phuong Trung Van) ;
  • Bui, Xuan Dieu (School of Applied Mathematics & Informatics Hanoi University of Science and Technology) ;
  • Vu, Trong Luong (VNU University of Education, Vietnam National University) ;
  • Nguyen, Van Minh (Department of Mathematics and Statistics University of Arkansas at Little Rock)
  • 투고 : 2019.07.12
  • 심사 : 2020.06.10
  • 발행 : 2020.06.30
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초록

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ+. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

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참고문헌

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