一类完全三阶边值问题的上下解方法  

The Upper and Lower Solution Method for a Class of Fully Third-Order Boundary Value Problems

作　　者：李嫣红 李永祥 LI Yanhong;LI Yongxiang(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gans)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《四川师范大学学报（自然科学版）》2018年第3期343-347,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11261053和11661071)

摘　　要：讨论完全三阶边值问题{-u'''(t)=f(t,u(t),u'(t),u″(t)),t∈[0,1],u(0)=u'(0)=u″(1)=0解的存在性与唯一性,其中f:[0,1]×R^3→R连续.在非线性项f(t,x,y,z)关于z满足适当的Nagumo条件下,运用特殊的截断技巧、Leray-Schauder不动点定理及上下解方法,获得了该方程解的存在性与唯一性结果.In this paper,we discuss the existence and uniqueness of solution for the fully third-order boundary value problems {-u″′（t）=f（t,u（t）,u′（t）,u″（t））,t∈[0,1], u（0）=u′（0）=u″（1）=0 where f：[0,1]×R^3→R is continuous.When f satisfies the proper Nagumo condition on z,we obtain the existence and uniqueness of solution for this equation via a special truncating technique,the Leray-Schauder fixed point theorem,and the lower and upper solution method.

关 键 词：完全三阶边值问题 上下解 NAGUMO条件 LERAY-SCHAUDER不动点定理 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]