On a fixed point theorem of mixed monotone operators and applications

Abstract

In this paper, by introducing $\tau-\varphi-$ mixed monotone operators in ordered Banach spaces, the existence and uniqueness theorems for the operators are obtained. In the end, the new results are used to study the existence of positive solutions to second order equations with Neumann boundary conditions.

Keywords

• mixed monotone operator
• fixed point theorem
• cone
• neumann boundary conditions