Previous |  Up |  Next

Article

Title: Bifurcation of periodic solutions in differential inclusions (English)
Author: Fečkan, Michal
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 42
Issue: 5
Year: 1997
Pages: 369-393
Summary lang: English
.
Category: math
.
Summary: Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems. (English)
Keyword: multivalued mappings
Keyword: differential inclusions
Keyword: periodic solutions
Keyword: dry friction terms
MSC: 34A47
MSC: 34A60
MSC: 34C23
MSC: 34C25
idZBL: Zbl 0903.34036
idMR: MR1467555
DOI: 10.1023/A:1023010108956
.
Date available: 2009-09-22T17:55:40Z
Last updated: 2020-07-02
Stable URL: http://hdl.handle.net/10338.dmlcz/134364
.
Reference: [1] A.A. Andronow, A.A. Witt, S.E. Chaikin: Theorie der Schwingungen I.Akademie Verlag, Berlin, 1965. MR 0216794
Reference: [2] N.V. Butenin, Y.I. Nejmark, N.A. Fufaev: An Introduction to the Theory of Nonlinear Oscillations.Nauka, Moscow, 1987. (Russian) MR 0929029
Reference: [3] C. Chicone: Lyapunov-Schmidt reduction and Melnikov integrals for bifurcation of periodic solutions in coupled oscillators.J. Differential Equations 112 (1994), 407–447. MR 1293477, 10.1006/jdeq.1994.1110
Reference: [4] K. Deimling: Multivalued Differential Equations.W. De Gruyter, Berlin, 1992. Zbl 0820.34009, MR 1189795
Reference: [5] K. Deimling: Multivalued differential equations and dry friction problems.Proc. Conf. Differential & Delay Equations, Ames, Iowa 1991, A. M. Fink, R. K. Miller, W. Kliemann (eds.), World Scientific, Singapore, 1992, pp. 99–106. Zbl 0820.34009, MR 1170147
Reference: [6] K. Deimling, P. Szilágyi: Periodic solutions of dry friction problems.Z. angew. Math. Phys. (ZAMP) 45 (1994), 53–60. MR 1259526, 10.1007/BF00942846
Reference: [7] K. Deimling, G. Hetzer, W. Shen: Almost periodicity enforced by Coulomb friction.Adv. Differential Equations 1 (1996), 265–281. MR 1364004
Reference: [8] J.P. Den Hartog: Mechanische Schwingungen.2nd ed., Springer-Verlag, Berlin, 1952. Zbl 0046.17201
Reference: [9] M. Fečkan: Bifurcation from homoclinic to periodic solutions in ordinary differential equations with multivalued perturbations.J. Differential Equations 130 (1996), 415–450. MR 1410897, 10.1006/jdeq.1996.0152
Reference: [10] M. Fečkan: Bifurcation from homoclinic to periodic solutions in singularly perturbed differential inclusions.Proceedings Royal Soc. Edinburgh A (to appear). MR 1465417
Reference: [11] J. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.Springer-Verlag, New York, 1983. MR 0709768
Reference: [12] P. Hartman: Ordinary Differential Equations.Wiley, New York, 1964. Zbl 0125.32102, MR 0171038
Reference: [13] H. Kauderer: Nichtlineare Mechanik.Springer-Verlag, Berlin, 1958. Zbl 0080.17409, MR 0145709
Reference: [14] K. Popp, P. Stelter: Stick-slip vibrations and chaos.Philos. Trans. R. Soc. London A 332 (1990), 89–105. 10.1098/rsta.1990.0102
Reference: [15] K. Popp: Some model problems showing stick-slip motion and chaos.ASME WAM, Proc. Symp. Friction-Induced Vibration, Chatter, Squeal and Chaos, R.A. Ibrahim and A. Soom (eds.) vol. DE-49, 1992, pp. 1–12.
Reference: [16] K. Popp, N. Hinrichs, M. Oestreich: Dynamical behaviour of a friction oscillator with simultaneous self and external excitation.Sādhanā 20, 2–4 (1995), 627–654. MR 1375904, 10.1007/BF02823210
Reference: [17] T. Pruszko: Some applications of the topological degree theory to multi-valued boundary value problems.Dissertationes Math. 229 (1984), 1–48. Zbl 0543.34008, MR 0741752
Reference: [18] T. Pruszko: Topological degree methods in multi-valued boundary value problems.Nonlinear Anal., Th., Meth. Appl. 5 (1981), 959–973. Zbl 0478.34017, MR 0633011, 10.1016/0362-546X(81)90056-0
Reference: [19] R. Reissig: Erzwungene Schwingungen mit zäher Dämpfung und starker Gleitreibung. II..Math. Nachr. 12 (1954), 119–128. MR 0069996, 10.1002/mana.19540120109
Reference: [20] R. Reissig: Über die Stabilität gedämpfter erzwungener Bewegungen mit linearer Rückstellkraft.Math. Nachr. 13 (1955), 231–245. Zbl 0066.33503, MR 0078535, 10.1002/mana.19550130310
Reference: [21] R. Rumpel: Singularly perturbed relay control systems.preprint (1996).
Reference: [22] K. Yosida: Functional Analysis.Springer-Verlag, Berlin, 1965. Zbl 0126.11504
.

Files

Files Size Format View
AplMat_42-1997-5_3.pdf 424.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo