一类三阶两点边值问题单调迭代正解的存在性  

Existence of Monotonic Iteration Positive Solutions for Three-order Two-point Boundary Value Problems

作　　者：孙博[1] 

机构地区：[1]中央财经大学应用数学学院,北京100081

出　　处：《工程数学学报》2009年第6期1027-1032,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10671012);国家教育部基金(20050007011)

摘　　要：本文利用锥上的不动点理论和单调迭代的方法研究了一类三阶两点边值问题单调迭代正解的存在性,得到了正解存在的充分条件,同时也给出了解的相应迭代序列来逼近解,并且给出了应用实例。值得一提的是,本文所讨论的边值问题中,非线性项显含未知函数的一阶和二阶导数。In this paper, we study the existence of monotonic iteration positive solutions for a kind of three-order two-point boundary value problems, the method mainly depends on the fixed point theory in cones and the iteration technique. We give the sufficient conditions for the existence of positive solutions to the boundary value problem and establish schemes for approximating the solution. An example is also given to illustrate the effectiveness of our results. It is worthwhile to mention that the nonlinear term in the equation we studied involves the first-and second-order derivatives explicitly.

关 键 词：正解 迭代解 锥 三阶两点边值问题 

分 类 号：O175.8[理学—数学]