On derivo-periodic multifunctions

Libor Jüttner

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

  • Volume: 21, Issue: 1, page 81-95
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Libor Jüttner. "On derivo-periodic multifunctions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.1 (2001): 81-95. <http://eudml.org/doc/271498>.

@article{LiborJüttner2001,
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.},
author = {Libor Jüttner},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {differential of multivalued functions; multivalued differential; contingent derivative; linearity of contingent derivative; periodic multivalued functions; derivo-periodic multivalued functions; derivo-periodic multifunctions; periodic derivative},
language = {eng},
number = {1},
pages = {81-95},
title = {On derivo-periodic multifunctions},
url = {http://eudml.org/doc/271498},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Libor Jüttner
TI - On derivo-periodic multifunctions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2001
VL - 21
IS - 1
SP - 81
EP - 95
AB - 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.
LA - eng
KW - differential of multivalued functions; multivalued differential; contingent derivative; linearity of contingent derivative; periodic multivalued functions; derivo-periodic multivalued functions; derivo-periodic multifunctions; periodic derivative
UR - http://eudml.org/doc/271498
ER -

References

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  1. [1] J. Andres, Derivo-periodic boundary value problems for nonautonomous ordinary differential equations, Riv. Mat. Pura Appl. 13 (1993), 63-90. Zbl0792.34016
  2. [2] J. Andres, Nonlinear rotations, Nonlin. Anal. 30 (1) (1997), 495-503. 
  3. [3] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984. 
  4. [4] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston 1990. 
  5. [5] H.T. Banks and M.Q. Jacobs, A differential calculus for multifunctions, J. Math. Anal. Appl. 29 (1970), 246-272. Zbl0191.43302
  6. [6] F.S. De Blasi, On the differentiability of multifunctions, Pacific J. Math. 66 (1) (1976), 67-81. Zbl0348.58004
  7. [7] M. Farkas, Periodic Motions, Springer, Berlin 1994. 
  8. [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. [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. Zbl0663.58006
  10. [10] M. Martelli and A. Vignoli, On differentiability of multi-valued maps, Bollettino U.M.I. 10 (4) (1974), 701-712. Zbl0311.46029
  11. [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. Zbl0980.34036
  12. [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. 

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