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2014 Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse
Zhenguo Luo, Liping Luo, Yunhui Zeng
J. Appl. Math. 2014: 1-12 (2014). DOI: 10.1155/2014/592513

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))))], ttk, kZ+; x(tk+)=x(tk-)+θk(x(tk)), kZ+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

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Zhenguo Luo. Liping Luo. Yunhui Zeng. "Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse." J. Appl. Math. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/592513

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010691
MathSciNet: MR3176824
Digital Object Identifier: 10.1155/2014/592513

Rights: Copyright © 2014 Hindawi

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