An intermediate value theorem for monotone operators in ordered Banach spaces
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Abstract
We consider a monotone increasing operator in an ordered Banach space having u
and u+ as a strong super- and subsolution, respectively. In contrast with the
well-studied case u+ < u , we suppose that u < u+. Under the assumption that the
order cone is normal and minihedral, we prove the existence of a fixed point located in the order interval [u , u+].
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Fixed point theory and applications, 2012, SpringerOpen, Heidelberg u.a., 2012, https://doi.org/10.1186/1687-1812-2012-211