A monotone method for constructing extremal solutions to second-order periodic boundary value problems

In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problemu″(t)=f(t,u,u′(t)), t∈[0,2π],u(0)=u(2π), u′(0)=u′(2π)in the presence of an upper solution β and a lower solution α with β⩽α.