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http://dx.doi.org/10.14403/jcms.2021.34.1.27

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

Ryu, Kimun (Department of Mathematics Education Cheongju University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.34, no.1, 2021 , pp. 27-35 More about this Journal
Abstract
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.
Keywords
T-periodic positive solution; ratio-dependent; predator-prey;
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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.   DOI
2 H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered banach spaces, SIAM Rev., 18 (1976), no. 4, 620-709.   DOI
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.   DOI
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.   DOI
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.