Taiwanese Journal of Mathematics

ON THE EXISTENCE OF PERIODIC SOLUTION FOR NEUTRAL DELAY COMPETITIVE SYSTEM

Zhanji Gui and Weigao Ge

Full-text: Open access

Abstract

In this paper, the $n-$species neutral delay competitive differential system with periodic coefficients is investigated by means of an abstract continuous theorem of $k-$set contractive operator and some analysis techniques. Sufficient conditions are obtained for periodic solution.

Article information

Source
Taiwanese J. Math., Volume 12, Number 2 (2008), 341-355.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574159

Digital Object Identifier
doi:10.11650/twjm/1500574159

Mathematical Reviews number (MathSciNet)
MR2402120

Zentralblatt MATH identifier
1153.34041

Subjects
Primary: 34B15: Nonlinear boundary value problems 35K13

Keywords
periodic solution $k-$Set contraction competitive system neutral delay equation

Citation

Gui, Zhanji; Ge, Weigao. ON THE EXISTENCE OF PERIODIC SOLUTION FOR NEUTRAL DELAY COMPETITIVE SYSTEM. Taiwanese J. Math. 12 (2008), no. 2, 341--355. doi:10.11650/twjm/1500574159. https://projecteuclid.org/euclid.twjm/1500574159


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References

  • B. G. Zhang and K. Gopalsamy, Global attractivity and oscillations in a periodic delay logistic equation, J. Math. Anal. Appl., 150 (1990), 274-283.
  • S. M. Lenhart and C. C. Travis, Global stability of a biological model with time delay, Proc. Amer. Math. Soc., 96 (1986), 75-78.
  • Y. Kuang, Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.
  • K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic publishers, Boston, 1992.
  • H. L. Smith, Population dynamics in daphnia magna, Ecology, 44 (1963), 651-653.
  • K. Gopalsamy, X. He and L. Wen, On a periodic neutral logistic equation, Glasgow Math. J. 33 (1991), 281-286.
  • H. I. Freedman and J. Wu, Periodic solutions of single-species models with periodic delay, SIAM J. Math. Anal., 23 (1992), 689-701.
  • B. R. Tang and Y. Kuang, Existence, uniqueness and asymptotic stability of periodic functional differential systems, Tohoku Math. J., 49 (1997), 217-239.
  • Y. Li, Positive periodic solutions for a neutral delay model, Acta. Math. Sinica, 39 (1996), 789-795.
  • Y. Li, Periodic solutions of a periodic neutral delay model, J. Math. Anal. Appl., 214 (1997), 11-21.
  • Y. Li, On a periodic neutral delay Lotka-Volterra system, Nonlinear Analysis, 39 (2000), 767-778.
  • Z. Yang and J. Cao, Sufficient conditions for the existence of positive periodic solutions of a class of neutral delay model, Appl. Math. Comput., 142 (2003), 123-142.
  • H. Fang and J. Li, On the existence of periodic solutions of a neutral delay model of single-species population growth, J. Math. Anal. Appl., 259 (2001), 8-17.
  • S. Lu, On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments, J. Math. Anal. Appl., 280 (2003), 321-333.
  • R. E. Gaines and J. L. Mawhin, Lectures Notes in Mathematics, Springer-verlag, Berlin, 1977, p. 568.
  • Z. Gui, Biological Dynamic Models and Computer Simulation, Science Press, Beijing, 2005.
  • W. V. Petryshynand and Z. S. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Analysis, 6 (1982), 943-969.
  • Z. Liu and Y. Mao, Existence theorem for periodic solutions of higher order nonlinear differential equations, J. Math. Anal. Appl., 216 (1997), 481-490.