Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 618413, 13 pages
doi:10.1155/2009/618413

Successive Iteration and Positive Solutions for Nonlinear m-Point Boundary Value Problems on Time Scales

Abstract

We study the existence of positive solutions for a class of m-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.