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Abstract and Applied Analysis
Volume 2009, Article ID 162891, 13 pages
Research Article

Existence and Uniqueness of Periodic Solutions of Mixed Monotone Functional Differential Equations

1Institute of Applied Mathematics, Shanxi Datong University, Datong, Shanxi 037009, China
2Department of Mathematics, Tsing Hua University, Hsinchu 30043, Taiwan

Received 21 April 2009; Accepted 3 July 2009

Academic Editor: Allan Peterson

Copyright © 2009 Shugui Kang and Sui Sun Cheng. 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.


This paper deals with the existence and uniqueness of periodic solutions for the first-order functional differential equation ๐‘ฆ ๎…ž ( ๐‘ก ) = โˆ’ ๐‘Ž ( ๐‘ก ) ๐‘ฆ ( ๐‘ก ) + ๐‘“ 1 ( ๐‘ก , ๐‘ฆ ( ๐‘ก โˆ’ ๐œ ( ๐‘ก ) ) ) + ๐‘“ 2 ( ๐‘ก , ๐‘ฆ ( ๐‘ก โˆ’ ๐œ ( ๐‘ก ) ) ) with periodic coefficients and delays. We choose the mixed monotone operator theory to approach our problem because such methods, besides providing the usual existence results, may also sometimes provide uniqueness as well as additional numerical schemes for the computation of solutions.