Monotone positive solution for three-point boundary value problem

In this paper, the existence of monotone positive solution for the following second-order three-point boundary value problem is studied: where η ∈ (0, 1), δ ∈ [0, ∞), f ∈ C([0, 1] × [0, ∞), [0, ∞)). Under certain growth conditions the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper. Supported by the Natural Science Foundation of Zhejiang Province of China (Y605144) and the XNF of Zhejiang University of Media and Communications (XN08001)