Geodesic
Existence and uniqueness of fixed points for mixed monotone operators with perturbations
Electronic journal of differential equations, Tome 2013 (2013)
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.
Classification : 47H07, 47H10, 34B10, 34B15
Keywords: sublinear, mixed monotone operator, normal cone, time scales, nonlinear integral equation 
@article{EJDE_2013__2013__a43,
     author = {Sang,  Yanbin},
     title = {Existence and uniqueness of fixed points for mixed monotone operators with perturbations},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1302.47078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a43/}
}
TY  - JOUR
AU  - Sang,  Yanbin
TI  - Existence and uniqueness of fixed points for mixed monotone operators with perturbations
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a43/
LA  - en
ID  - EJDE_2013__2013__a43
ER  - 
%0 Journal Article
%A Sang,  Yanbin
%T Existence and uniqueness of fixed points for mixed monotone operators with perturbations
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a43/
%G en
%F EJDE_2013__2013__a43
Sang,  Yanbin. Existence and uniqueness of fixed points for mixed monotone operators with perturbations. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a43/