FIXED POINT THEOREMS IN ORDERED METRIC SPACES AND APPLICATIONS TO NONLINEAR BOUNDARY VALUE PROBLEMS.

In this paper, we extend the concept of mixed monotone mappings and then we consider certain fixed point theorems for a pair of mappings in metric spaces with a partial ordering. As an application, we study existence of solutions for the following fourth-order two-point boundary value problems for elastic beam equations:... where f is a continuous mapping of [0, 1]×R×R into R. Moreover, using these fixed point theorems, we prove several existence results for the solutions of various boundary value problems. [ABSTRACT FROM AUTHOR]