Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

Abstract

The existence of nondecreasing positive solutions for the nonlinear third-order two-point boundary value problem u‴(t) + q(t)f(t, u(t), u′(t)) = 0, 0 < t < 1, u(0) = u″(0) = u′ (1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.