Periodic boundary value problem for differential equations with delay and monotone iterative method (Q1821249)

Consider the delay-differential equation (1) \(x'=f(t,x,x_ t)\), subject to the boundary condition (2) \(x(0)=x(2\pi)\) where \(f\in C[J\times R\times {\mathcal C},R]\), \(I=[0,2\pi]\), \({\mathcal C}=C[[-\tau,0],R]\), \(\tau >0\). The authors study the existence of extremal solutions of periodic boundary value problem (1)-(2). The method of lower and upper solutions coupled with the monotone iterative technique is used to establish the main result.