The Bolzano-Poincar\'e-Miranda theorem in infinite dimensional Banach spaces
Functional Analysis
2018-07-04 v1
Abstract
We study the existence of zeroes of mappings defined in Banach spaces. We obtain, in particular, an extension of the well-known Bolzano-Poincar\'e-Miranda theorem to infinite dimensional Banach spaces. We also establish a result regarding the existence of periodic solutions to differential equations posed in an arbitrary Banach space.
Keywords
Cite
@article{arxiv.1807.01043,
title = {The Bolzano-Poincar\'e-Miranda theorem in infinite dimensional Banach spaces},
author = {David Ariza-Ruiz and Jesús Garcia-Falset and Simeon Reich},
journal= {arXiv preprint arXiv:1807.01043},
year = {2018}
}