Positive Solution of a class of Three-point Semi-positone Boundary Value Problem

In the paper,by using a fixed point theorems in cones,a class of second order three-point semi-positone boundary value problem was studied as following: (p(t)u′(t))′+λf(t,u)=0,0t1P(o)u′(0)=0,u(1)=ku(η)If nonlinearity satisfies Caratheodory's conditions,the above boundary value problem has a positive solution for sufficiently small where it doesn't require to be continuous and to have lower bound.