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

作　　者：祁卫杰[1] 贾梅[1] 王淑[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《吉林大学学报（理学版）》2012年第6期1103-1108,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11171220);上海市教委科研创新基金重点项目(批准号:10ZZ93)

摘　　要：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.

关 键 词：上下解方法 单调迭代法 边值问题 积分边界条件 

分 类 号：O175.8[理学—数学]