충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제34권1호
  • /
  • Pages.27-35
  • /
  • 2021
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

EXISTENCE OF POSITIVE T-PERIODIC SOLUTIONS OF RATIO-DEPENDENT PREDATOR-PREY SYSTEMS

  • Ryu, Kimun (Department of Mathematics Education Cheongju University)
  • 투고 : 2021.01.07
  • 심사 : 2021.01.11
  • 발행 : 2021.02.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We study the existence of positive T-periodic solutions of ratio-dependent predator-prey systems with time periodic and spatially dependent coefficients. The fixed point theorem by H. Amann is used to obtain necessary and sufficient conditions for the existence of positive T-periodic solutions.

키워드

참고문헌

  1. S. Ahmad and A. C. Lazer, Asymptotic behavior of solutions of periodic competition diffusion systems, Nonlinear Anal.-Theory Methods Appl., 13 (1989), 263-283. https://doi.org/10.1016/0362-546X(89)90054-0
  2. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered banach spaces, SIAM Rev., 18 (1976), no. 4, 620-709. https://doi.org/10.1137/1018114
  3. K. J. Brown and P. Hess, Positive periodic solutions of predator-prey reactiondiffusion systems, Nonlinear Anal.-Theory Methods Appl., 16 (1991), Ser. A: Theory Methods, 1147-1158. https://doi.org/10.1016/0362-546X(91)90202-C
  4. Y. Du, Positive periodic solutions of a competitor-competitor-mutualist model, Differ. Integral Equ., 9 (1996), no. 5, 1043-1066.
  5. A. Ghoreishi and R. Logan, Positive solutions to a system of periodic parabolic partial differential equations, Differ. Integral Equ., 9 (1996), no. 3, 607-618.
  6. P. Hess, Periodic-parabolic boundary value problems and positivity, Pitman Research Notes in Math. Ser. 247, Longman Sci. and Tech., Harlow, Essex, UK, 1991.
  7. W. Ko and K. Ryu, Positive periodic solutions of a Hassell-Varley type predatorprey system, Indian J. Pure Appl. Math., 44 (2013), no. 6, 865-882. https://doi.org/10.1007/s13226-013-0047-2
  8. J. Lopez-Gomez, Positive periodic solutions of Lotka-Volterra reaction-diffusion systems, Differ. Integral Equ., 5 (1992), 55-72.
  9. C. V. Pao, On nonlinear parabolic and elliptic equations, Plenum Press, New York, 1992.