Existence and uniqueness of fixed points for monotone operators in partially ordered Banach spaces and applications

In this paper, we employ partial order method, cone theory, and the techniques of measure of weak noncompactness to prove several new theorems on the existence and the uniqueness of fixed points or coupled fixed points for operators satisfying some monotonicity assumptions. Our conclusions generalize and improve several well-known results. As an application, we investigate the existence of a unique solution for a class nonlinear second-order ordinary differential equations. We also discuss the existence of a unique solution for a system of integral equations.