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Periodic solutions of isotone hybrid systems
1. | Department of Mathematics and Statistics, University of Maryland Baltimore County (UMBC), Baltimore, MD 21250, United States |
2. | Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117 Berlin, Germany |
References:
[1] |
G. Birkhoff, "Lattice Theory," $2^{nd}$ rev. ed., Amer. Math. Soc. Colloq. Publ., 25 AMS, Providence, 1948. |
[2] |
A. Friedman and L.-S. Jiang, Periodic solutions for a thermostat control problem, Comm. PDE, 13 (1988), 515-550. |
[3] |
K. Glashoff and J. Sprekels, The regulation of temperature by thermostats and set-valued integral equations, J. Int. Eqns., 4 (1982), 95-112. |
[4] |
G. Gripenberg, On periodic solutions of a thermostat equation, SIAM J. Math. Anal., 18 (1987), 694-702. |
[5] |
F. Hante, G. Leugering and T. I. Seidman, An augmented BV setting for feedback switching control, J. Systems Sci. & Comp., 23 (2010), 456-466.
doi: 10.1007/s11424-010-0140-0. |
[6] |
L. T. Izu, W. G. Wier, and C. W. Balke, Evolution of cardiac calcium waves from stochastic calcium sparks, Biophysical Journal, 80 (2001), 103-120.
doi: 10.1016/S0006-3495(01)75998-X. |
[7] |
M. A. Krasnosel'skiĭ and A. V. Pokrovskiĭ, Periodic oscillations in systems with relay nonlinearities, (transl. from (MR0355210), DAN USSR, 216 (1974), 733-736). Soviet Math Doklady, 15 (1974), 873-877. |
[8] |
M. A. Krasnosel'skiĭ and A .V. Pokrovskiĭ, "Systems with Hysteresis," (transl. of "Sistemy s Gisterezisom'', Nauka, Moscow, 1983) Springer-Verlag, Berlin, 1989. |
[9] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Translations of Math. Monographs, vol. 23, Amer. Math. Soc., Providence, 1968. |
[10] |
T. I. Seidman, Switching systems: thermostats and periodicity, Report MRR-83-07, UMBC, 1983, Available from: http://www.math.umbc.edu/~seidman/papers.html |
[11] |
T. I. Seidman, Switching systems I, Control and Cybernetics, 19 (1990), 63-92. |
[12] |
T. I. Seidman, Switching systems and periodicity, in "Nonlinear Semigroups, PDE, and Attractors'' (eds. T. E. Gill and W. W. Zachary), LCM \#1394; Springer-Verlag, New York, (1989), 199-210. |
[13] |
B. Stoth, "Periodische Lösungen Von Linearen Thermostat Problemen," Diplomthesis: (Report SFB 256), Univ. Bonn, 1987. |
[14] |
W. Szczechla, "Periodicity for Certain Switching Systems," Ph.D thesis, UMBC, 1993. |
show all references
References:
[1] |
G. Birkhoff, "Lattice Theory," $2^{nd}$ rev. ed., Amer. Math. Soc. Colloq. Publ., 25 AMS, Providence, 1948. |
[2] |
A. Friedman and L.-S. Jiang, Periodic solutions for a thermostat control problem, Comm. PDE, 13 (1988), 515-550. |
[3] |
K. Glashoff and J. Sprekels, The regulation of temperature by thermostats and set-valued integral equations, J. Int. Eqns., 4 (1982), 95-112. |
[4] |
G. Gripenberg, On periodic solutions of a thermostat equation, SIAM J. Math. Anal., 18 (1987), 694-702. |
[5] |
F. Hante, G. Leugering and T. I. Seidman, An augmented BV setting for feedback switching control, J. Systems Sci. & Comp., 23 (2010), 456-466.
doi: 10.1007/s11424-010-0140-0. |
[6] |
L. T. Izu, W. G. Wier, and C. W. Balke, Evolution of cardiac calcium waves from stochastic calcium sparks, Biophysical Journal, 80 (2001), 103-120.
doi: 10.1016/S0006-3495(01)75998-X. |
[7] |
M. A. Krasnosel'skiĭ and A. V. Pokrovskiĭ, Periodic oscillations in systems with relay nonlinearities, (transl. from (MR0355210), DAN USSR, 216 (1974), 733-736). Soviet Math Doklady, 15 (1974), 873-877. |
[8] |
M. A. Krasnosel'skiĭ and A .V. Pokrovskiĭ, "Systems with Hysteresis," (transl. of "Sistemy s Gisterezisom'', Nauka, Moscow, 1983) Springer-Verlag, Berlin, 1989. |
[9] |
O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Translations of Math. Monographs, vol. 23, Amer. Math. Soc., Providence, 1968. |
[10] |
T. I. Seidman, Switching systems: thermostats and periodicity, Report MRR-83-07, UMBC, 1983, Available from: http://www.math.umbc.edu/~seidman/papers.html |
[11] |
T. I. Seidman, Switching systems I, Control and Cybernetics, 19 (1990), 63-92. |
[12] |
T. I. Seidman, Switching systems and periodicity, in "Nonlinear Semigroups, PDE, and Attractors'' (eds. T. E. Gill and W. W. Zachary), LCM \#1394; Springer-Verlag, New York, (1989), 199-210. |
[13] |
B. Stoth, "Periodische Lösungen Von Linearen Thermostat Problemen," Diplomthesis: (Report SFB 256), Univ. Bonn, 1987. |
[14] |
W. Szczechla, "Periodicity for Certain Switching Systems," Ph.D thesis, UMBC, 1993. |
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