Almost periodic solutions of periodic systems governed by subdifferential operators

Ôtani, Mitsuharu

doi:10.1090/S0002-9939-1995-1242102-4

Almost periodic solutions of periodic systems governed by subdifferential operators
HTML articles powered by AMS MathViewer

by Mitsuharu Ôtani

Proc. Amer. Math. Soc. 123 (1995), 1827-1832

DOI: https://doi.org/10.1090/S0002-9939-1995-1242102-4

PDF | Request permission

Abstract:

We construct an example of the periodic evolution system governed by the time-dependent subdifferential operators admitting almost periodic orbits which are not quasiperiodic.

References

Luigi Amerio and Giovanni Prouse, Almost-periodic functions and functional equations, Van Nostrand Reinhold Co., New York-Toronto-Melbourne, 1971. MR 0275061, DOI 10.1007/978-1-4757-1254-4
J. B. Baillon and A. Haraux, Comportement à l’infini pour les équations d’évolution avec forcing périodique, Arch. Rational Mech. Anal. 67 (1977), no. 1, 101–109 (French). MR 493553, DOI 10.1007/BF00280830

Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

M. L. Cartwright, Almost periodic flows and solutions of differential equations, Proc. London Math. Soc. (3) 17 (1967), 355–380; corrigenda, ibid. 17 (1967), 768. MR 223649, DOI 10.1112/plms/s3-17.4.768-s
M. L. Cartwright, Almost periodic differential equations and almost periodic flows, J. Differential Equations 5 (1969), 167–181. MR 239191, DOI 10.1016/0022-0396(69)90110-7
A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799, DOI 10.1007/BFb0070324
Alain Haraux and Mitsuharu Ôtani, Quasi-periodicity of bounded solutions to some periodic evolution equations, J. Math. Soc. Japan 42 (1990), no. 2, 277–294. MR 1041226, DOI 10.2969/jmsj/04220277
Nobuyuki Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math. 22 (1975), no. 3-4, 304–331. MR 399662, DOI 10.1007/BF02761596

Solvability of nonlinear evolution equations with time-dependent constrains and applications

30

Nobuyuki Kenmochi and Mitsuharu Ôtani, Instability of periodic solutions of some evolution equations governed by time-dependent subdifferential operators, Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), no. 1, 4–7. MR 798024
Nobuyuki Kenmochi and Mitsuharu Ôtani, Asymptotic behavior of periodic systems generated by time-dependent subdifferential operators, Funkcial. Ekvac. 29 (1986), no. 2, 219–236. MR 877431
G. C. O’Brien, The frequencies of almost periodic solutions of almost periodic differential equations, J. Austral. Math. Soc. 17 (1974), 332–344. Collection of articles dedicated to the memory of Hanna Neumann, VII. MR 0357979, DOI 10.1017/S1446788700017092
Mitsuharu Ôtani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, periodic problems, J. Differential Equations 54 (1984), no. 2, 248–273. MR 757295, DOI 10.1016/0022-0396(84)90161-X
Mitsuharu Ôtani, Nonlinear evolution equations with time-dependent constraints, Adv. Math. Sci. Appl. 3 (1993/94), no. Special Issue, 383–399. MR 1287937
Yoshio Yamada, Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries, Nagoya Math. J. 70 (1978), 111–123. MR 492875, DOI 10.1017/S0027763000021814