Positive solutions for some boundary value problems via a new fixed point theorem

In this paper, we establish some new fixed point theorems of mixed monotone operator with a perturbation. Moreover, we prove the existence and the uniqueness of positive solutions of a second order Neumann boundary value problem, a second order Sturm Liouville boudary value problem and a nonlinear elliptic boundary value problem for the Lane-Emden-Fowler equation.