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Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

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Listed:
  • Zhenguo Luo
  • Liping Luo
  • Yunhui Zeng

Abstract

By using a fixed point theorem of strict‐set‐contraction, which is different from Gaines and Mawhin′s continuation theorem and abstract continuation theory for k‐set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x′(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x′(t-γ1(t,x(t))),…,x′(t-γm(t,x(t))))], t≠tk, k∈Z+; x(tk+)=x(tk-)+θk(x(tk)), k∈Z+. As applications of our results, we also give some applications to several Lotka‐Volterra models and new results are obtained.

Suggested Citation

  • Zhenguo Luo & Liping Luo & Yunhui Zeng, 2014. "Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:592513
    DOI: 10.1155/2014/592513
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    1. Zhenguo Luo & Liping Luo, 2013. "Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    2. Zhenguo Luo & Liping Luo, 2013. "Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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