Electron. J. Diff. Equ., Vol. 2013 (2013), No. 233, pp. 1-16.

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

Yanbin Sang

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.

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Yanbin Sang
Department of Mathematics, North University of China
Taiyuan, Shanxi, 030051, China
email: syb6662009@yahoo.com.cn, Tel +86 351 3923592

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