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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
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.

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  • A. Lasota and Aaron Strauss, Asymptotic behavior for differential equations which cannot be locally linearized, J. Differential Equations 10 (1971), 152–172. MR 277837, DOI
  • S. N. Chow, L. A. Karlovitz, and A. Lasota, An integral form of the mean value theorem for nondifferentiable mappings, J. Math. Anal. Appl. 38 (1972), 214–222. MR 305066, DOI
  • A. Granas, Introduction to topology of functional spaces, Math. Lecture Notes, University of Chicago, Chicago, Ill., 1961.
  • M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, The Macmillan Co., New York, 1964. Translated by A. H. Armstrong; translation edited by J. Burlak; A Pergamon Press Book. MR 0159197
  • A. Lasota and Z. Opial, An application of the Kakutani—Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 781–786 (English, with Russian summary). MR 196178
  • O. Nicoletti, Sulle condizioni iniziali che determinano gli integrali delle equazioni differenziali ordinaire, Atti. Accad. Sci. Torino 33 (1897/98), 746-759.
  • Stanisław Kasprzyk and Józef Myjak, On the existence of solutions of the Floquet problem for ordinary differential equations, Zeszyty Nauk. Uniw. Jagielloń. Prace Mat. 13 (1969), 35–39. MR 247172
  • A. Lasota and Z. Opial, Sur la dépendance continue des solutions des équations différentielles ordinaires de leurs seconds membres et des conditions aux limites, Ann. Polon. Math. 19 (1967), 13–36 (French). MR 208042, DOI

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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