A quasilinearization method for second-order four-point boundary value problems

In this paper, we obtain the existence and uniqueness results for general second-order four-point boundary value problems by applying the method of upper and lower solutions together with Leray–Schauder degree. Also we obtain monotone iteration schemes which converge quadratically to the unique solution of some specific second-order four-point boundary value problems by using the method of quasilinearization.