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Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

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  • Hui-Sheng Ding
  • Julio G. Dix

Abstract

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett‐Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for the n‐dimensional functional difference system y(k + 1) = A(k)y(k) + f(k, y(k − τ)), k ∈ ℤ, where A(k) is not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results.

Suggested Citation

  • Hui-Sheng Ding & Julio G. Dix, 2014. "Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:659152
    DOI: 10.1155/2014/659152
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    References listed on IDEAS

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    1. Guang Zhang & Sui Sun Cheng, 2002. "Positive periodic solutions of nonautonomous functional differential equations depending on a parameter," Abstract and Applied Analysis, John Wiley & Sons, vol. 7(5), pages 279-286.
    2. Wei Chen & Lijuan Wang, 2012. "Positive Periodic Solutions of Nicholson‐Type Delay Systems with Nonlinear Density‐Dependent Mortality Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Guang Zhang & Sui Sun Cheng, 2002. "Positive periodic solutions of nonautonomous functional differential equations depending on a parameter," Abstract and Applied Analysis, Hindawi, vol. 7, pages 1-8, January.
    4. Wei Chen & Lijuan Wang, 2012. "Positive Periodic Solutions of Nicholson-Type Delay Systems with Nonlinear Density-Dependent Mortality Terms," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, December.
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    Cited by:

    1. Yue-Wen Cheng & Hui-Sheng Ding, 2014. "Multiple Positive Periodic Solutions for a Functional Difference System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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