Successive iteration technique for singular nonlinear system with four-point boundary conditions

Abstract

In this paper, the existence of at least one positive solution of the system of singular differential equations with four-point coupled boundary conditions is discussed. A constructive monotonic iterative technique on the equivalent completely continuous nonlinear operator is used to establish the result. This method produces an approximate solution in the form of series which is very helpful in developing a numerical scheme for the positive solution of the system. It is demonstrated through the examples.