Journal of Applied Mathematics

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

Zhenguo Luo, Liping Luo, and Yunhui Zeng

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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 - τ 1 ( t , x ( t ) ) ) , , x ( t - τ n ( t , x ( t ) ) ) , x ' ( t - γ 1 ( t , x ( t ) ) ) , , x ' ( t - γ m ( t , x ( t ) ) ) ) ] ,   t t k ,   k Z + ;   x ( t k + ) = x ( t k - ) + θ k ( x ( t k ) ) ,   k Z + . As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 592513, 12 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305566

Digital Object Identifier
doi:10.1155/2014/592513

Mathematical Reviews number (MathSciNet)
MR3176824

Zentralblatt MATH identifier
07010691

Citation

Luo, Zhenguo; Luo, Liping; Zeng, Yunhui. Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse. J. Appl. Math. 2014 (2014), Article ID 592513, 12 pages. doi:10.1155/2014/592513. https://projecteuclid.org/euclid.jam/1425305566


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