非线性二阶三点边值问题的存在性原理

An Existence Theory of Nonlinear Second-order Three-Point Boundary Value

应用Leray-Schauder抉择和锥不动点定理,建立了非线性二阶三点边值问题{y"+f(t,y)=0,0<t<1 y(0)=a,y(1)-ξy(c)=b,0<ξ<1,0<c<1的正解存在性定理,其中非线性项f不允许在y=0处具有奇性。

In this paper, existence theory for positive solution is presented to nonlinear three-point boundry value problem {y＂＋f（t,y）=0,0〈t〈1 y（0）=a,y（1）-ζy（c）=b,0〈ζ〈1, 0〈c〈1 The function shall not be singular at. The existence of solutions is obtained via the Leray-Shauder altemative and the fixed point theorem in cones.