Geodesic
Existence and uniqueness of fixed points for mixed monotone operators with perturbations
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a143,
     author = {Sang, Yanbin},
     title = {Existence and uniqueness of fixed points for mixed monotone operators with perturbations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a143/}
}
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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__a143/