Abstract: Using the new truncation function technique and the method of upper and lower solutions, we discussed the existence of solutions for the fully third-order boundary value problem:{u(t)=f(t,u(t),u′(t),u″(t)),t∈［0,1］,u(0)=u′(1)=u″(1)=0,where f: ［0,1］×3→was a continuous function. Under the condition that the nonlinear term f satisfied some inequalities, we gave the existence of solutions to the problem. In particular, we obtained the existence of the positive solutions to the problem when the nonlinear term f was not required to be non-negative.

Key words: fully third-order boundary value problem, existence, upper solution, lower solution, positive solution