Download PDF - On derivo-periodic multifunctionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On derivo-periodic multifunctions

Authors 1

Affiliations

  1. Department of Mathematics Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic

Abstract

The problem of linearity of a multivalued derivative and consequently the problem of necessary and sufficient conditions for derivo-periodic multifunctions are investigated. The notion of a derivative of multivalued functions is understood in various ways. Advantages and disadvantages of these approaches are discussed.

Keywords

ENG
differential of multivalued functions, multivalued differential, contingent derivative, linearity of contingent derivative, periodic multivalued functions, derivo-periodic multivalued functions

Bibliography

  1. J. Andres, Derivo-periodic boundary value problems for nonautonomous ordinary differential equations, Riv. Mat. Pura Appl. 13 (1993), 63-90.
  2. J. Andres, Nonlinear rotations, Nonlin. Anal. 30 (1) (1997), 495-503.
  3. J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
  4. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston 1990.
  5. H.T. Banks and M.Q. Jacobs, A differential calculus for multifunctions, J. Math. Anal. Appl. 29 (1970), 246-272.
  6. F.S. De Blasi, On the differentiability of multifunctions, Pacific J. Math. 66 (1) (1976), 67-81.
  7. M. Farkas, Periodic Motions, Springer, Berlin 1994.
  8. J.S. Cook, W.H. Louisell and W.H. Yocom, Stability of an electron beam on a slalom orbit, J. Appl. Phys. 29 (1958), 583-587.
  9. G. Fournier and D. Violette, A fixed point theorem for a class of multi-valued continuously differentiable maps, Anal. Polon. Math. 47 (1987), 381-402.
  10. M. Martelli and A. Vignoli, On differentiability of multi-valued maps, Bollettino U.M.I. 10 (4) (1974), 701-712.
  11. J. Mawhin, From Tricomi's equation for synchronous motors to the periodically forced pendulum, In Tricomi's Ideas and Contemporary Applied Mathematics, Atti Conv. Lincei 147, Accad. Naz. Lincei (Roma), (1998), 251-269.
  12. P. Meystre, Free-electron Lasers, An Introduction, 'Laser Physics (D.F. Walls and J.D. Harvey, ed.)', Academic Press, Sydney-New York-London-Toronto-San Francisco 1980.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2001/21/1
Export to PBN, Opens in new tab
Pages:
81-95
Main language of publication
English
Received
2000-06-09
Published
2001

DOI: 10.7151/dmgt.1018

Exact and natural sciences