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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 760918, 8 pages
http://dx.doi.org/10.1155/2012/760918
Research Article

Periodic Solutions for Duffing Type 𝑝 -Laplacian Equation with Multiple Constant Delays

1College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, Hunan 415000, China
2College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China

Received 19 November 2011; Accepted 17 January 2012

Academic Editor: Elena Braverman

Copyright © 2012 Hong Zhang and Junxia Meng. 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

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing type 𝑝 -Laplacian equation with multiple constant delays of the form ( 𝜑 𝑝 ( 𝑥 ( 𝑡 ) ) ) + 𝐶 𝑥 ( 𝑡 ) + 𝑔 0 ( 𝑡 , 𝑥 ( 𝑡 ) ) + 𝑛 𝑘 = 1 𝑔 𝑘 ( 𝑡 , 𝑥 ( 𝑡 𝜏 𝑘 ) ) = 𝑒 ( 𝑡 ) . Moreover, an example is provided to illustrate the effectiveness of the results in this paper.