An intermediate value theorem in ordered Banach spaces

Details An intermediate value theorem in ordered Banach spaces An intermediate value theorem in ordered Banach spaces

2012-03-14

arxiv.org/abs/1203.3068v1

Mathematics

Functional Analysis

Scientific paper

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 ordered interval $[u_-,u_+].$

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