一类无穷区间上的三阶两点边值问题解的存在性  

Existence of Solutions for a Third-Order Two-Point Boundary Value Problem on Infinite Intervals

作　　者：杨赞 裴明鹤[2] Yang Zan;Pei Minghe(Tongji Zhejiang College,Jiaxing 314051,China;School of Mathematics and Statistics,Beihua University,Jilin 132013,China)

机构地区：[1]同济大学浙江学院,浙江嘉兴314051 [2]北华大学数学与统计学院,吉林吉林132013

出　　处：《北华大学学报（自然科学版）》2017年第6期710-718,共9页Journal of Beihua University（Natural Science）

基　　金：吉林省教育厅科学技术研究项目(2016-45)

摘　　要：研究一类无穷区间上的三阶两点边值问题:{x′″(t)+a(t)f(t,x(t),x'(t),x″(t))=0,t∈(0,+∞),x(0)=0,x'(0)-bx″(0)=0,x″(+∞)=c,其中a∈C([0,+∞),(0,+∞)),f∈C([0,+∞)×R^3,R),b≥0,c∈R.综合运用上下解方法和Schauder不动点定理,得到了上述三阶无穷边值问题解的存在性.We concerned with a third-order two-point boundary value problem on infinite intervals of the form x?(t)+a(t)f(t,x(t),x′(t),x″(t))=0,t∈(0,+￥),x(0)=0,x′(0)-bx″(0)=0,x″(+￥)=c,{where a∈C([0,+∞),(0,+∞)),f∈C([0,+∞)×R3,R),b≥0,c∈R.The existence of solution is obtained by using the upper and lower solution method together with Schauder fixed point theorem for the above third-order infinite boundary value problem.

关 键 词：三阶无穷边值问题 上下解方法 SCHAUDER不动点定理 存在性 

分 类 号：O175.8[理学—数学]