An intermediate value theorem for monotone operators in ordered Banach spaces
1 FB 08 - Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, Mainz, D-55099, Germany
2 Department of Mathematics, University of Uppsala, P.O. Box 480, Uppsala, S-75106, Sweden
Fixed Point Theory and Applications 2012, 2012:211 doi:10.1186/1687-1812-2012-211Published: 22 November 2012
We consider a monotone increasing operator in an ordered Banach space having and as a strong super- and subsolution, respectively. In contrast with the well-studied case , we suppose that . Under the assumption that the order cone is normal and minihedral, we prove the existence of a fixed point located in the order interval .
MSC: 47H05, 47H10, 46B40.