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An implicit function theorem for nondifferentiable mappings


Authors: Shui Nee Chow and A. Lasota
Journal: Proc. Amer. Math. Soc. 34 (1972), 141-146
MSC: Primary 34A10; Secondary 46G05
DOI: https://doi.org/10.1090/S0002-9939-1972-0291527-7
MathSciNet review: 0291527
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Abstract: By using Borsuk’s antipodal theorem, an implicit function theorem for nondifferentiable mappings in Banach spaces is proved. Applications of this theorem to give existence and continuous dependence on a parameter of solutions of certain boundary value problems, are shown.


References [Enhancements On Off] (What's this?)

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Keywords: Implicit function theorem, multivalued derivatives, completely continuous mappings, Borsuk antipodal theorem, boundary value problems, Nicoletti problem, aperiodic boundary condition
Article copyright: © Copyright 1972 American Mathematical Society