Journal of the
Korean Mathematical Society JKMS

In this paper, we consider an impulsive nonlinear second order ordinary differential equation with nonlinear three-point boundary conditions and develop a monotone iteration scheme by relaxing the convexity assumption on the function involved in the differential equation and the concavity assumption on nonlinearities in the boundary conditions. In fact, we obtain monotone sequences of iterates (approximate solutions) converging quadratically to the unique solution of the impulsive three-point boundary value problem.

Keywords: quasilinearization, three-point boundary value problems, quadratic convergence

MSC numbers: 34A37, 34B10, 34B15