Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Uniqueness theorem for a Cauchy problem
with hysteresis

Author: Jana Kopfová
Journal: Proc. Amer. Math. Soc. 127 (1999), 3527-3532
MSC (1991): Primary 34A12; Secondary 34A60
Published electronically: August 5, 1999
MathSciNet review: 1694870
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Cauchy problem for an ordinary differential equation coupled with a hysteresis operator is studied. Under physically reasonable assumptions on the forcing term, uniqueness of solutions is shown without assuming Lipschitz continuity of the hysteresis curves. The result is true for any kind of hysteresis operators with monotone curves of motion.

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

  • 1. V.Chernorutskii and D.Rachinskii, On uniqueness of an initial-value problem for ODE with hysteresis, Nonl. Diff. Equ. Appl. 4, 1997, 391-399. MR 98j:34004
  • 2. P.Hartman, Ordinary Differential Equations, Birkhäuser, 1982. MR 83e:34002
  • 3. M.A.Krasnosel'skii and A.V.Pokrovskii, Systems with Hysteresis, Springer-Verlag, Berlin, 1989. MR 90a:93001
  • 4. A.Visintin, Differential Models of Hysteresis, Springer-Verlag, Berlin, 1995. MR 96h:47001
  • 5. A.A.Vladimirov, M.A.Krasnosel'skii, and V.V.Chernorutskii, The Cauchy problem for systems with hysteresis, Russian Acad. Sci. Dokl. Math. 48 (1994), 502-506. MR 94k:47104

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34A12, 34A60

Retrieve articles in all journals with MSC (1991): 34A12, 34A60

Additional Information

Jana Kopfová
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Address at time of publication: Slezska Univerzita, Matematicky ustav, Bezrucovo nam. 13, 746 01 Opava, Czech Republic

Received by editor(s): October 11, 1996
Published electronically: August 5, 1999
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society