Owing to the importance of a class of second order differential equations problems in physics and mechanics,the existence and multiplicity of the solutions to those problems have been studied by many scholars.By changing differential equations into nonlinear integral equation,we study the existence of positive solution of a class of second order differential equations problems by the fixed point theorem of cone expansion and compression,and the fixed point index theorem,then we obtain two multiple positive solutions theorems under some conditions,and give the proof of main lemmas that are important to our discussion.