On derivo-periodic multifunctions
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 1, pp. 81-95.

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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.
Keywords: differential of multivalued functions, multivalued differential, contingent derivative, linearity of contingent derivative, periodic multivalued functions, derivo-periodic multivalued functions
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Jüttner, Libor. On derivo-periodic multifunctions. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/DMDICO_2001_21_1_a2/

[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.