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This article has been retracted since the limits of the three sequences included in the manuscript are likely to be the same, which cannot be ruled out in the proof. So, the three nontrivial homoclinic solutions in Theorem 15 are likely to be the same one.

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  1. J. Guo and B. Dai, “Three homoclinic solutions for second-order p-Laplacian differential system,” Abstract and Applied Analysis, vol. 2013, Article ID 183585, 10 pages, 2013.
Abstract and Applied Analysis
Volume 2013, Article ID 183585, 10 pages
Research Article

Three Homoclinic Solutions for Second-Order -Laplacian Differential System

School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China

Received 13 May 2013; Revised 23 July 2013; Accepted 31 July 2013

Academic Editor: M. Victoria Otero-Espinar

Copyright © 2013 Jia Guo and Bin-Xiang Dai. 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.


We consider second-order -Laplacian differential system. By using three critical points theorem, we establish the new criterion to guarantee that this -Laplacian differential system has at least three homoclinic solutions. An example is presented to illustrate the main result.