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Mathematical Problems in Engineering
Volume 2017, Article ID 5041783, 5 pages
Research Article

Multiple Periodic Solutions for a Class of Second-Order Neutral Impulsive Functional Differential Equations

1College of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, China
2Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China
3Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, China

Correspondence should be addressed to Jingli Xie; moc.361@421127ilgnijeix

Received 29 August 2016; Revised 1 December 2016; Accepted 20 December 2016; Published 12 January 2017

Academic Editor: Olfa Boubaker

Copyright © 2017 Jingli Xie 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.


In this paper, we study a class of second-order neutral impulsive functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of critical point theory and variational methods. We propose an example to illustrate the applicability of our result.