Monotone Technique for Periodic Solutions of Differential Equations
Abstract
**Please note that the full text is embargoed** ABSTRACT: The existence of periodic solutions has received
a great deal of attention in recent years [1,7-11,14]. In [8,11] the existence of solutions of first
and second order PBVP (periodic boundary
value problem) has been studied successfully
by combining the two basic techniques, namely,
the method of lower and upper solutions
and the Lyapunov-Schmidt method. In [6,11-13]
monotone methods are developed for obtaining
extremal solutions of BVP as limits of monotone
iterates. In the first order PBVP [11] the
monotone method has a greater significance
since each member of the sequence is a periodic
solution of a first order linear equation
which can be explicitly computed. In this article,
we give a survey of the current state of art of this
important method for first and second order
PBVP. Our result in [11,13] indicate that this
approach is useful to study semilinear parabolic
IBVP and other problems at resonance. For the
extension of monotone method to finite systems
of PBVP, see [15] and to abstract PBVP, see [7].