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arXiv · 1807.01043

The Bolzano-Poincar\'e-Miranda theorem in infinite dimensional Banach spaces

David Ariza-Ruiz·Jesús Garcia-Falset·Simeon Reich
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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.

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David Ariza-Ruiz, Jesús Garcia-Falset, Simeon Reich. 2018-07-03. The Bolzano-Poincar\'e-Miranda theorem in infinite dimensional Banach spaces. https://arxiv.org/abs/1807.01043

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