二阶三点边值问题的正解（英文）  

Positive solutions for a second-order three-point boundary value problem

作　　者：刘健[1] 封汉颍[1] 

机构地区：[1]军械工程学院基础部,石家庄050003

出　　处：《黑龙江大学自然科学学报》2015年第3期325-329,共5页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundation of Hebei Province(A2012506010)

摘　　要：研究下列二阶三点边值问题x″(t)+f(t,x)=0,0<t<1,x(0)=0,x(1)=δx(η)改造边值问题的方程,计算在边界条件下的格林函数并给出其性质。应用锥拉伸压缩不动点定理,研究正解的存在性。与目前已有研究在非共振情形0<δη<1和共振情形δη=1时得到的结果相比,考虑η∈(0,1),δ>0。在一些条件下,本研究得到的结果同时包括了非共振和共振情形。The second-order three-point boundary value problem x″（t）＋f（t,x）=0,0〈t〈1, x（0）=0,x（1）=δx（η） is studied. The equation is firstly reconstructed, then the Green＇ s function of that SUbject to the boundary conditions and its properties are given. Then, the existence of positive solutions is investigated by applying of the fixed point theorem in cones. Comparing with the recent results given in non-resonance cases 0〈δη〈1 or in resonance cases δη=1, the case η∈（0,1）,δ〉0 is considered here. The result including non-resonance and resonance cases is given under some conditions.

关 键 词：三点边值问题 不动点定理 正解 

分 类 号：O175.8[理学—数学]