二阶三点边值问题两个正解的存在性  

Existence of Double Positive Solutions of Two-order Three-point Boundary Value Problem

作　　者：续晓欣[1] 梁月亮[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2009年第2期105-109,共5页Journal of North University of China(Natural Science Edition)

摘　　要：利用Guo-Krasnoseskill’s锥拉伸与锥压缩型不动点定理及格林函数的性质,研究了非线性二阶三点边值问题,获得了其正解存在性的新结果.在此基础上,给出了此边值问题两个正解存在性的几个充分条件,推广和改进了以前文献的相关结果,因此本文在边值问题的进一步研究方面具有一定的理论意义.A class of nonlinear two-order three-point boundary value problem is considered, and the existence of positive solutions is obtained by making use of the Guo-Krasnoseskill＇s fixed point theorem of cone expansion-compression type and the properties of the Green function. On the basis of that, several sufficient conditions of the existence of double positive solutions are deduced for the nonlinear two-order three-point boundary value problem. The results have generalized and improved the related ones of the known references, which has theoretical significance on problem boundary value.

关 键 词：边值问题 不动点定理 两个正解 

分 类 号：O175.8[理学—数学]