n阶微分方程边值问题解的存在性和唯一性

Existence and Uniqueness of the Solutions of nth-Order Differential Equations Boundary Value Problems

运用上下解方法和单调迭代法研究一类含有积分边界条件的n阶微分方程边值问题解的存在性和唯一性,得到了解的存在性和唯一性的充分条件,给出了求近似解的单调迭代格式,并在满足解的存在、唯一性条件下给出了求解迭代序列的误差估计式.

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.