Eigenvalue of fourth-order m-point boundary value problem with derivatives

This paper deals with the existence of positive solutions for the fourth-order nonlinear ordinary differential equation subject to the boundary conditions: where α,β,γ,δ≥0 are constants such that ρ=αδ+αγ+βδ>0, and . By means of a fixed-point theorem due to Krasnaselskii, some new existence results of positive solutions for the above multi-point boundary value problem are obtained, which improve the main results of Graef et al. [J.R. Graef, C. Qian, B. Yang, A three-point boundary value problem for nonlinear fourth-order differential equations, J. Math. Anal. Appl. 287 (2003) 217–233]. An example is given to demonstrate the main results of this paper.