Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 233, pp. 1-16.

Title: Existence and uniqueness of fixed points for mixed monotone
       operators with perturbations

Author: Yanbin Sang  (North Univ. of China, Taiyuan, Shanxi, China)

Abstract:
 In this article, we study a class of mixed monotone
 operators with perturbations. Using a monotone iterative technique and
 the properties of cones, we show the existence and uniqueness 
 for fixed points for such operators.
 As applications, we prove the existence and uniqueness of positive
 solutions for nonlinear integral equations of second-order on time
 scales. In particular, we do not assume the existence of upper-lower
 solutions or compactness or continuity conditions.

Submitted April 10, 2013. Published October 18, 2013.
Math Subject Classifications: 47H07, 47H10, 34B10, 34B15.
Key Words: Sublinear; Mixed monotone operator; normal cone; time scales; 
           nonlinear integral equation.