New fixed point theorems for mixed monotone operators and local existence-uniqueness of positive solutions for nonlinear boundary value problems (Q549797)

The authors first present a fixed point theorem for mixed monotone operators defined on cones of Banach spaces; by mixed monotone operator, it is meant an operator \(A\) increasing in one variable and decreasing in the other one. Then they study the eigenvalue problem \(A(x,x)=\lambda x\). As application, the authors develop several existence-uniqueness theorems for some BVPs with various boundary conditions. These theorems are illustrated by means of concrete examples.