Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An implicit function theorem for nondifferentiable mappings
HTML articles powered by AMS MathViewer

by Shui Nee Chow and A. Lasota PDF
Proc. Amer. Math. Soc. 34 (1972), 141-146 Request permission

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
  • 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 10.1016/0022-0396(71)90103-3
  • 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 10.1016/0022-247X(72)90130-8
  • 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, A Pergamon Press Book, The Macmillan Company, New York, 1964. Translated by A. H. Armstrong; translation edited by J. Burlak. 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 10.4064/ap-19-1-13-36
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34A10, 46G05
  • Retrieve articles in all journals with MSC: 34A10, 46G05
Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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