Abstract:

Using upper and lower solution method and the monotone iterative method, we studied the existence and uniqueness of the solutions of nth-order differential equations boundary value problems with integral boundary conditions. We obtained the sufficient conditions of the existence and uniqueness of solutions, and  gave the iterative sequence for solving the solutions and its error estimation formula under satisfying the conditions of uniqueness of solutions.

Key words: upper and lower solutions method, monotone iterative method; boundary value problems, integral boundary conditions