Quasilinearization of dynamic equations on time scales involving the sum of three functions

Abstract

In this paper, we present and discuss a method of quasilinearization, coupled with the method of upper and lower solutions for the solutions of a class of two-point boundary value problem of dynamic equations on time scales concerning the sum of three functions. A monotone iterative scheme whose elements converge rapidly to the unique solution of the problem is established, and the convergence is shown to be of order k + 1 (k >= 1).