On the existence of periodic solutions to nonlinear abstract parabolic equations

Hiroko OKOCHI

doi:10.2969/jmsj/04030541

Hiroko OKOCHI

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 3 Pages 541-553

DOI https://doi.org/10.2969/jmsj/04030541

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Published: 1988 Received: November 12, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. F. Ames, Nonlinear partial differential equations in engineering, Academic Press, New York, 1965.
2) J. B. Baillon and A. Haraux, Conpoertement a l'infini pour les équations d'évolutionavec forcing periodic, Arch. Rational Mech. Anal., 67 (1977), 101-109.
3) V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Groningen, 1976.
4) P. Benilan and H. Brezis, Solutions fables d'équations d'évolution dans les espaces de Hilbert, Ann. Inst. Fourier, 22 (1972), 311-329.
5) F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc., 72 (1966), 571-575.
6) G. Gripenberg, On the asymptotic behavior of nonlinear contraction semigroups, Math. Scand., 44 (1979), 385-397.
7) A. Haraux, Equations d'evolution nonlinéars: solutions linéaires et periodiques, Ann. Inst. Fourier, 28 (1978), 201-220.
8) A. Haraux, Nonlinear evolution equations, Lecture Notes in Math., 841, Springer, 1981.
9) T. Nagai, Periodic solutions for certain time-dependent parabolic variational inequalities, Hiroshima Math. J., 5 (1975), 537-549.
10) H. Okochi, A note on asymptotic strong convergence of nonlinear contraction semigroups, Proc. Japan Acad., 56 (1980), 83-84.
11) Y. Yamada, On evolution equations generated by subdifferential operators, J. Fac. Sci. Univ. Tokyo, 23 (1976), 491-515.
12) Y. Yamada, Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries, Nagoya Math. J., 70 (1978), 111-123.

Right : [1] W. F. Ames, Nonlinear partial differential equations in engineering, Academic Press, New York, 1965.
[2] J. B. Baillon and A. Haraux, Conpoertement a l'infini pour les équations d'évolution avec forcing periodic, Arch. Rational Mech. Anal., 67 (1977), 101-109.
[3] V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Groningen, 1976.
[4] P. Benilan and H. Brezis, Solutions fables d'équations d'évolution dans les espaces de Hilbert, Ann. Inst. Fourier, 22 (1972), 311-329.
[5] F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc., 72 (1966), 571-575.
[6] G. Gripenberg, On the asymptotic behavior of nonlinear contraction semigroups, Math. Scand., 44 (1979), 385-397.
[7] A. Haraux, Equations d'evolution nonlinéars: solutions linéaires et periodiques, Ann. Inst. Fourier, 28 (1978), 201-220.
[8] A. Haraux, Nonlinear evolution equations, Lecture Notes in Math., 841, Springer, 1981.
[9] T. Nagai, Periodic solutions for certain time-dependent parabolic variational inequalities, Hiroshima Math. J., 5 (1975), 537-549.
[10] H. Okochi, A note on asymptotic strong convergence of nonlinear contraction semigroups, Proc. Japan Acad., 56 (1980), 83-84.
[11] Y. Yamada, On evolution equations generated by subdifferential operators, J. Fac. Sci. Univ. Tokyo, 23 (1976), 491-515.
[12] Y. Yamada, Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries, Nagoya Math. J., 70 (1978), 111-123.

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