关键词: 奇异半正边值问题, 锥, 正解, 不动点定理

Abstract:

By using the fixed point index theory, the authors investigate the existence of multiple positive solutions for third-order three-point singular semipositone BVP
{x'''(t)-f(t, x)=0,    t ∈(0, 1);
 x(0)=x'(η)=x''(1)=0, 1/2 < η <1,
The nonlinear term f (t, x) may be singular at t =0,  t =1, and x =0, also may be negative for some values of  t and  x.

Key words: Singular semipositone boundary value problem, Cone, Positive solution, Fixed point theorem