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

摘要

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(4)(t)=f(t,u(t),u″(t)),t∈[0,2π],u(0)=u(2π),u′(0)=u′(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.