二阶线性常微分方程m点边值问题的正解  

Positive solutions for second order ordinary differential equation m-point boundary value problems

作　　者：刘锐[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《华中师范大学学报（自然科学版）》2003年第4期464-467,共4页Journal of Central China Normal University：Natural Sciences

基　　金：宁夏自然科学基金资助项目(1999A002).

摘　　要：建立了m点边值问题u″+a(t)f(u)=0,u(0)=0,u(1)- m-2i=1αiu(ηi)=b正解的存在性,其中b,αi>0,ηi∈(0,1),i=1,…,m-2为已知,且 m-2i=1αiηi<1,在适当的条件下证明了:存在一个正数b*,使得上述问题对于0<b<b*至少有一个正解,对于b>b*无解.The existence of positive solutions for the m-point boundary value problem(u″+ a(t))f(u)=0, u(0)=0, u(1)-m-2i=1α_iu(η_i)=b, is established in this paper, where b, α_i>0, η_i∈(0,1), i=1,..., m-2,m-2i=1α_iη_i<1 are given. Under suitable conditions it shows that there exists a positive number b~* such that the problem has at least one positive solution for 0<b<b~*and no solution for b>b~*.

关 键 词：M点边值问题 正解 SCHAUDER不动点定理 

分 类 号：O175.1[理学—数学]