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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1018, author = {Libor J\"uttner}, title = {On derivo-periodic multifunctions}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {21}, year = {2001}, pages = {81-95}, zbl = {0997.26020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1018} }
Libor Jüttner. On derivo-periodic multifunctions. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 21 (2001) pp. 81-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1018/
[000] [1] J. Andres, Derivo-periodic boundary value problems for nonautonomous ordinary differential equations, Riv. Mat. Pura Appl. 13 (1993), 63-90. | Zbl 0792.34016
[001] [2] J. Andres, Nonlinear rotations, Nonlin. Anal. 30 (1) (1997), 495-503.
[002] [3] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
[003] [4] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston 1990.
[004] [5] H.T. Banks and M.Q. Jacobs, A differential calculus for multifunctions, J. Math. Anal. Appl. 29 (1970), 246-272. | Zbl 0191.43302
[005] [6] F.S. De Blasi, On the differentiability of multifunctions, Pacific J. Math. 66 (1) (1976), 67-81. | Zbl 0348.58004
[006] [7] M. Farkas, Periodic Motions, Springer, Berlin 1994.
[007] [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.
[008] [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. | Zbl 0663.58006
[009] [10] M. Martelli and A. Vignoli, On differentiability of multi-valued maps, Bollettino U.M.I. 10 (4) (1974), 701-712. | Zbl 0311.46029
[010] [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. | Zbl 0980.34036
[011] [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.