Monotone Method for Second Order Periodic Boundary Value Problems
Abstract
**Please note that the full text is embargoed** ABSTRACT: In recent years, there has been an extensive study of the existence of periodic solutions [1,8-11,14,15]. In, [8,11], the existence of solutions of first and second order PBVP (periodic boundary value problems) has been obtained
by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems (Lyapunov-Schmidt method), which provide conditions that are easily verifiable and which covers previous known results of other authors. As a constructive method for obtaining extremal solutions
of initial and boundary value problems, the monotone iterative procedure has been employed by several researchers [5-7,11-13,15]. The objective of this
paper is to employ this useful technique for second order MAT to obtain the minimal
and maximal solutions as limits of monotone iterates. Our method can be used to study semilinear parabolic initial boundary value problems and other problems at resonance.