English

An intermediate value theorem in ordered Banach spaces

Functional Analysis 2013-01-29 v1

Abstract

We consider a monotone increasing operator in an ordered Banach space having uu_- and u+u_+ as a strong super- and subsolution, respectively. In contrast with the well studied case u+<uu_+ < u_-, we suppose that u<u+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+].[u_-,u_+].

Keywords

Cite

@article{arxiv.1203.3068,
  title  = {An intermediate value theorem in ordered Banach spaces},
  author = {Vadim Kostrykin and Anna Oleynik},
  journal= {arXiv preprint arXiv:1203.3068},
  year   = {2013}
}
R2 v1 2026-06-21T20:33:52.400Z