Existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions

This paper is concerned with the existence of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. By applying monotone iteration method, we not only obtain the existence of monotone positive solutions but also establish iterative schemes for approximating the solutions. It is worth mentioning that these iterative schemes start offwith zero function or quadratic function, which is very useful and feasible for computational purpose. An example is also included to illustrate the main results obtained.