Existence Of Positive And Multi-positive Solutions For Nonlinear Three-Point Boundary Value Problems At Resonance

The paper is concerned with the existence of positive and multi-positive solutions for a nonlinear second order three-point boundary value problems of differential equation at resonance by using Krasnoselskii fixed point theorem.Firstly,whenwe can transform the resonant probleminto the non-resonant problemSecondly,we show that the existence of positive solutions is equal to the existence of nonzero fixed points for the integral operator. This part is the core of the whole paper for the following aspects:l.The calculative process of Green-Function is very complex,2.The estimating process of upper and lower bounds to Green-Function is of necessity and full of techniques.Finally,we get the existence theorems of positive and multi-positive solutions by using Krasnoselskii fixed point theorem.