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Journal of Applied Mathematics
Volume 2014, Article ID 592513, 12 pages
http://dx.doi.org/10.1155/2014/592513
Research Article

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

1Department of Mathematics, National University of Defense Technology, Changsha 410073, China
2Department of Mathematics, Hengyang Normal University, Hengyang 421008, China

Received 29 June 2013; Revised 8 November 2013; Accepted 11 November 2013; Published 27 February 2014

Academic Editor: Chein-Shan Liu

Copyright © 2014 Zhenguo Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -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: . As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.