Summary: We study positive solutions for the second order three-point boundary value problem:
where , , and , , , are continuous. Based on a new extension of Krasnoselskii fixed-point theorem (which was established by Y. Guo and W. Ge [J. Math. Anal. Appl. 290, No. 1, 291–301 (2004; Zbl 1054.34023)], the existence of positive solutions for the boundary value problems is obtained. In particular, we obtain the Green function of the problem, which makes the problem simpler.