Abstract and Applied Analysis
Volume 2009 (2009), Article ID 162891, 13 pages
doi:10.1155/2009/162891
Existence and uniqueness of periodic solutions of mixed monotone functional differential equations
Shugui Kang1
and Sui Sun Cheng2
1Institute of Applied Mathematics, Shanxi Datong University, Datong, Shanxi 037009, China
2Department of Mathematics, Tsing Hua University, Hsinchu 30043, Taiwan
Abstract
This paper deals with the existence and uniqueness of periodic solutions for the first-order functional differential equation y′(t)=−a(t)y(t)+f1(t,y(t−τ(t)))+f2(t,y(t−τ(t))) 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.