New existence and uniqueness results for an elastic beam equation with nonlinear boundary conditions

In this article, we study the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions, and some sufficient conditions which guarantee the existence of unique monotone positive solution are established. The methods employed are two fixed point theorems for mixed monotone operators with perturbation. Our results can not only guarantee the existence of unique monotone positive solution, but also be applied to construct an iterative scheme for approximating it. Two examples are given to illustrate our main results.