一类奇异二阶三点边值方程组正解的存在性

Existence of Positive Solutions for Singular Systems of Three-Point Boundary Value Problems

利用锥上的不动点定理,研究了下列奇异非线性二阶三点边值方程组-u″=f(t,v),t∈(0,1)-v″=g(t,v),t∈(0,1)u′(0)=v′(0)=0,u(1)=αu(η),v(1)=αv(η)其中η∈(0,1),0<α<1,在某些较弱条件下正解的存在性。

[Abstract] In this paper, by using the fixed point method, we get the existence of positive solutions to the three-point boundary value problem for a second order differential equation system in some weak conditions -/μ^N=f（t,υ）,t∈（O,1）-υ^=g（t,υ）,t∈（0,1）,μ^1（0）=υ＇（0）=0,μ（1）=aμ（η）,υ（1）=υ＇（η） ∈（0,1）,0〈υ〈1