Abstract: The existence of positive solution to some two-point boundary value problems are considered for third-order nonlinear ordinary differential equation.This class of boundary value problems arises from the investigation for flow of sticky liquid and possesses wide application in liquid mechanics.In recent years,Professor Jiang Daqing has obtained the existence of positive solution under the condition where nonlinear term is superlinear or sublinear.By improving the method used by Jiang,the author give two existence theorems of the class of problems under the condition where the nonlinear term is neither superlinear nor sublinear.The processes are as follows: (1) By applying the Green functions of corresponding boundary value problems the problems are transformed to integral equations on the space of continuous functions; (2) By applying the properties of Green functions the suitable cones are chosen; (3) By making use of Krasnoselskii fixed point theorem of cone expansion-compression type,two existence theorems of positive solution are obtained.This paper implies that Jiang’s main conclusions are the special cases of our results.

Key words: third-order two-point boundary value problem, nonlinear equation, positive solution, existence theorem