非线性三阶三点边值问题的单调正解  

Monotone Positive Solution for Nonlinear Third-Order Three-Point Boundary Value Problems

作　　者：武晨[1] WU Chen(Basic Courses Teaching Department,Branch of Nanjing Jiangsu Union Technical Institute,Nanjing 210019,China)

机构地区：[1]江苏联合职业技术学院南京分院基础课程教学部

出　　处：《南通大学学报（自然科学版）》2019年第1期83-88,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：江苏省教育科学“十三五”规划课题(B-b/2016/03/55);江苏省职业教育教学改革研究课题(ZZZ5)

摘　　要：考虑了一类三阶三点边值问题{u'''(t)+λa(t)f(t,u(t),u'(t))=0,t∈(0,1)U(0)=u'(0)=0,u'(1)=au'(η)解的存在性,其中η∈(0,1),α∈[0,1/η)为常数,λ∈(0,+∞)是一个参数。通过Guo-KrasnoselsKii不动点定理,得到了若干关于上述边值问题单调正解存在性和不存在性的准则。In this paper,the existence of positive solution to the following third-order three-point boundary value problems is studied:{u'''(t)+λa(t)f(t,u(t),u'(t))=0,t∈(0,1)U(0)=u'(0)=0,u'(1)=au'(η),where η∈(0,1),α∈[0,1/η) are constants,λ∈(0,+∞) is a positive parameter.By using Guo-KrasnoselsKii fixed-point theorem,the new existence and nonexistence of results are obtained.

关 键 词：三阶三点边值问题 单调正解 Guo-KrasnoselsKii不动点定理 

分 类 号：O175.8[理学—数学]