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Dissipative periodic processes. (English) Zbl 0274.34061


MSC:

37-XX Dynamical systems and ergodic theory
34K20 Stability theory of functional-differential equations
34G99 Differential equations in abstract spaces
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[1] Jack K. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39 – 59. · Zbl 0179.13303
[2] Marshall Slemrod, Asymptotic behavior of periodic dynamical systems on Banach spaces, Ann. Mat. Pura Appl. (4) 86 (1970), 325 – 330. · Zbl 0205.43105
[3] Constantine M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971), 239 – 252; erratum, ibid. 10 (1971), 179 – 180. · Zbl 0236.34038
[4] Marianito Cruz A. and Jack K. Hale, Stability of functional differential equations of neutral type, J. Differential Equations 7 (1970), 334 – 355. · Zbl 0191.38901
[5] M. Slemrod and E. F. Infante, An invariance principle for dynamical systems on Banach space: application to the general problem of thermoelastic stability, Instability of continuous systems (IUTAM Sympos., Herrenalb, 1969), Springer, Berlin, 1971, pp. 215 – 221.
[6] Constantine M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37 (1970), 297 – 308. · Zbl 0214.24503
[7] Marshall Slemrod, Nonexistence of oscillations in a nonlinear distributed network, J. Math. Anal. Appl. 36 (1971), 22 – 40. · Zbl 0217.29103
[8] J. E. Billotti, Dissipative functional differential equations, Ph.D. Dissertation, Brown University, Providence, R. I., 1969.
[9] Norman Levinson, Transformation theory of non-linear differential equations of the second order, Ann. of Math. (2) 45 (1944), 723 – 737. · Zbl 0061.18910
[10] R. Ressig, G. Sansone and R. Conti, Nichtlineare Differential gleichungen höhrer Ordnung, Edizioni Cremonese, Roma, 1969.
[11] V. A. Pliss, Nonlocal problems of the theory of oscillations, Translated from the Russian by Scripta Technica, Inc. Translation edited by Harry Herman, Academic Press, New York-London, 1966. · Zbl 0151.12104
[12] Felix E. Browder, On a generalization of the Schauder fixed point theorem, Duke Math. J. 26 (1959), 291 – 303. · Zbl 0086.10203
[13] Taro Yoshizawa, Asymptotic stability of solutions of an almost periodic system of functional-differential equations, Rend. Circ. Mat. Palermo (2) 13 (1964), 209 – 221. · Zbl 0132.06602
[14] Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, No. 9, The Mathematical Society of Japan, Tokyo, 1966.
[15] G. Stephen Jones, Asymptotic fixed point theorems and periodic systems of functional-differential equations, Contributions to Differential Equations 2 (1963), 385 – 405.
[16] G. Stephen Jones, Periodic motions in Banach space and applications to functional-differential equations, Contributions to Differential Equations 3 (1964), 75 – 106.
[17] Jack K. Hale, Synchronization by diffusive coupling, Proceedings of the Conference ”Topological Methods in Differential Equations and Dynamical Systems” (Kraków-Przegorzały, 1996), 1998, pp. 17 – 31. · Zbl 1002.34035
[18] J. P. LaSalle, A study of synchronous asymptotic stability, Ann. of Math. (2) 65 (1957), 571 – 581. · Zbl 0080.07301
[19] Taro Yoshizawa, Extreme stability and almost periodic solutions of functional-differential equations, Arch. Rational Mech. Anal. 17 (1964), 148 – 170. · Zbl 0132.06601
[20] J. P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968), 57 – 65. · Zbl 0159.12002
[21] Jack K. Hale, Geometric theory of functional-differential equations, Differential Equations and Dynamical Systems (Proc. Internat. Sympos., Mayaguez, P.R., 1965) Academic Press, New York, 1967, pp. 247 – 266.
[22] V. Lakshmikantham and S. Leela, Differential and integral inequalities. Vol. II, Academic Press, New York, 1969. · Zbl 0177.12403
[23] J. K. Hale, Lectures on functional differential equations, University of California, Los Angeles, Calif., 1968/69.
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