一类二阶非线性边值问题的正解

Positive Solutions for a Class of Second-Order Nonlinear Boundary Value Problem

利用Kransnosel′skii锥拉伸锥压缩不动点定理及不动点指数理论,讨论了一类二阶非线性边值问题u″+a(t) f (u) =0 ,t∈(0 ,1 ) ,αu(0 ) -βu′(0 ) =0 ,γu(1 ) +δu′(1 ) =0 正解的存在性与多重性.函数a允许在端点t=0和t=1具有奇性.

The existence and multiplicity of positive solutions for second-order nonlinear boundary value problems u″+a(t)f(u)=0, t∈(0,1), αu(0)-βu′(0)=0, γu(1)+δu′(1)=0 are studied by using the Kransnosel′skii fixed-point theorem of cone expansion-compression type and the fixed-point index results, where a is allowed to be singular at both end points t=0 and t=1.