非线性二阶三点边值问题系统正解的存在性  

Positive Solutions to System of Nonlinear Second-Order Three-Point Boundary Value Problem

作　　者：王静[1] 何明霞[1] 

机构地区：[1]甘肃联合大学师范学院,兰州730000

出　　处：《应用泛函分析学报》2013年第3期265-271,共7页Acta Analysis Functionalis Applicata

基　　金：甘肃省教育厅科研项目(1013B-03)

摘　　要：考虑二阶三点边值问题系统-u″=f(t,v),t∈(0,1),-v″=g(t,u),t∈(0,1),u(0)=αu(η),u(1)=βu(η),v(0)=αv(η),v(1)=βv(η),其中f,g∈C([0,1]×R^+,R^+),g(t,0)≡0,η∈(0,1)且0<β≤α<1.首先给出了线性边值问题的Green函数;其次,给出了Green函数的一些很好的性质;最后,运用锥上拉伸与压缩不动点定理研究了上述边值问题系统至少一个或多个正解的存在性.In this paper,we investigate the following system of nonlinear second-order three-point boundary value problems — u~' = f(t,v),t ∈(0,1),— v″ = g(t,u),t ∈(0,1),u(0) = αu(η),u(1) =βu(η),u(0) = av(η),v(1) = βv(η),where f,g ∈C([0,1]x R^+,R^+),g{t,0)≡ 0,η∈(0,1) and0 <β≤α < 1.First,Green's function for associated liner boundary value problem is constructed;next,several useful properties of the Green's function are obtained;in the last place,some existence and multiplicity criteria of positive solutions are established by using the fixed point theorems of cone expansion and compression.

关 键 词：系统 二阶三点边值问题 正解 不动点 锥 

分 类 号：O175[理学—数学]