半正二阶三点边值问题正解的存在性

Existence of Positive Solution for Semipositone Second-order Three-point Boundary Value Problem

运用锥上的拉伸与压缩不动点定理证明了半正二阶三点边值问题u″(t)+fλ(t,u(t))=0,0<t<1,u(0)=αu(η),u(1)=βu(η)至少一个正解的存在性.

The paper studies the existence of positive solution for the semipositone second-order three- point boundary value problem u″（t）＋λf（t,u（t）） = 0,0 〈 t 〈 1 ,u（0） = au （η）,u（1） =βu（η） . Our arguments are based on the well-known Guo-Krasnosel＇skii fixed-point theorem in cones.