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

Zhenguo Luo, Liping Luo and Yunhui Zeng

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/592513

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:592513

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