The Bolzano-Poincaré-Miranda theorem in infinite dimensional Banach spaces (1807.01043v1)

Published 3 Jul 2018 in math.FA

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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