The Method of upper and lower solutions for second-order non-homogeneous two-point boundary-value problem

This paper studies the existence and uniqueness of solutions for a type of second-order two-point boundary-value problem depending on the first-order derivative through a non-linear term. By constructing a special cone and using the upper and lower solutions method, we obtain the sufficient conditions of the existence and uniqueness of solutions, and a monotone iterative sequence solving the boundary-value problem. An error estimate formula is also given under the condition of a unique solution.