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Volumn 56, Issue 1, 2004, Pages 247-268

Massera’s theorem for almost periodic solutions of functional differential equations

Author keywords

Abstract functional differential equation; Almost periodic solutions; Decomposition; Massera s theorem; Variation of constants formula

Indexed keywords


EID: 1842766368     PISSN: 00255645     EISSN: 18811167     Source Type: Journal    
DOI: 10.2969/jmsj/1191418705     Document Type: Article
Times cited : (44)

References (41)
  • 1
    • 0012014599 scopus 로고
    • Geometrical methods in the theory of ordinary differential equations, Second edition
    • Springer-Verlag, New York-Berlin
    • V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Second edition, Grundlehren Math. Wiss., 250, Springer-Verlag, New York-Berlin, 1988.
    • (1988) Grundlehren Math. Wiss. , pp. 250
    • Arnold, V.I.1
  • 3
    • 0003327379 scopus 로고    scopus 로고
    • Evolution Semigroups in Dynamical Systems and Differential Equations
    • American Mathematical Society, Providence, RI
    • C. Chicone and Yu. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Math. Surveys Monogr., 70, American Mathematical Society, Providence, RI, 1999.
    • (1999) Math. Surveys Monogr. , pp. 70
    • Chicone, C.1    Latushkin, Y.U.2
  • 4
    • 0002433520 scopus 로고
    • Strongly limit-compact maps
    • S. N. Chow and J. K. Hale, Strongly limit-compact maps, Funkcial. Ekvac., 17 (1974), 31-38.
    • (1974) Funkcial. Ekvac. , vol.17 , pp. 31-38
    • Chow, S.N.1    Hale, J.K.2
  • 5
    • 0003872825 scopus 로고
    • Abstract Evolution Equations, Periodic Problems and Applications
    • Longman, New York
    • D. Daners and P. K. Medina, Abstract Evolution Equations, Periodic Problems and Applications, Pitman Research Notes in Math. Ser., volume 279, Longman, New York, 1992.
    • (1992) Pitman Research Notes in Math. Ser. , vol.279
    • Daners, D.1    Medina, P.K.2
  • 6
    • 0003451928 scopus 로고
    • Almost Periodic Differential Equations
    • Springer, Berlin-New York
    • A. M. Fink, Almost Periodic Differential Equations, Lecture Notes in Math., 377, Springer, Berlin-New York, 1974.
    • (1974) Lecture Notes in Math. , pp. 377
    • Fink, A.M.1
  • 7
    • 0037139632 scopus 로고    scopus 로고
    • Boundedness and almost periodicity of solutions of partial functional differential equations
    • T. Furumochi, T. Naito and N. V. Minh, Boundedness and almost periodicity of solutions of partial functional differential equations, J. Differential Equations, 180 (2002), 125-152.
    • (2002) J. Differential Equations , vol.180 , pp. 125-152
    • Furumochi, T.1    Naito, T.2    Minh, N.V.3
  • 8
    • 0009806827 scopus 로고    scopus 로고
    • Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations
    • G. Guhring and F. Rabiger, Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations, Abstr. Appl. Anal., 4 (1999), 169-194.
    • (1999) Abstr. Appl. Anal. , vol.4 , pp. 169-194
    • Guhring, G.1    Rabiger, F.2
  • 11
    • 0002513583 scopus 로고
    • Phase space for retarded equations with infinite delay
    • J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41.
    • (1978) Funkcial. Ekvac. , vol.21 , pp. 11-41
    • Hale, J.K.1    Kato, J.2
  • 12
    • 0002087589 scopus 로고
    • On the existence of periodic solutions for linear inhomogeneous and quasilinear functional differential equations
    • L. Hatvani and T. Krisztin, On the existence of periodic solutions for linear inhomogeneous and quasilinear functional differential equations, J. Differential Equations, 97 (1992), 1-15.
    • (1992) J. Differential Equations , vol.97 , pp. 1-15
    • Hatvani, L.1    Krisztin, T.2
  • 13
    • 0000748245 scopus 로고
    • Periodic solutions of quasi-linear partial functional differential equations with unbounded delay
    • H. R. Henriquez, Periodic solutions of quasi-linear partial functional differential equations with unbounded delay, Funkcial. Ekvac., 37 (1994), 329-343.
    • (1994) Funkcial. Ekvac. , vol.37 , pp. 329-343
    • Henriquez, H.R.1
  • 14
    • 0003460899 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer-Verlag, Berlin-New York
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer-Verlag, Berlin-New York, 1981.
    • (1981) Lecture Notes in Math. , pp. 840
    • Henry, D.1
  • 15
    • 0004408787 scopus 로고
    • Periodic solutions of a linear Volterra system, Differential equations, Xanthi
    • Y. Hino and S. Murakami, Periodic solutions of a linear Volterra system, Differential equations, Xanthi, 1987, Lecture Notes in Pure and Appl. Math., 118 (1987), 319-326.
    • (1987) Lecture Notes in Pure and Appl. Math. , vol.118 , pp. 319-326
    • Hino, Y.1    Murakami, S.2
  • 16
    • 0003287113 scopus 로고
    • Functional Differential Equations with Infinite Delay
    • Springer-Verlag, Berlin-New York
    • Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Math., 1473, Springer-Verlag, Berlin-New York, 1991.
    • (1991) Lecture Notes in Math. , pp. 1473
    • Hino, Y.1    Murakami, S.2    Naito, T.3
  • 17
    • 0037050698 scopus 로고    scopus 로고
    • A variation of constants formula for abstract functional differential equations in Banach spaces
    • Y. Hino, S. Murakami, T. Naito and N. V. Minh, A variation of constants formula for abstract functional differential equations in Banach spaces, J. Differential Equations, 179 (2002), 336-355.
    • (2002) J. Differential Equations , vol.179 , pp. 336-355
    • Hino, Y.1    Murakami, S.2    Naito, T.3    Minh, N.V.4
  • 19
    • 22844456811 scopus 로고    scopus 로고
    • On a question in the theory of almost periodic differential equations
    • Z. S. Hu and A. B. Mingarelli, On a question in the theory of almost periodic differential equations, Proc. Amer. Math. Soc., 127 (1999), 2665-2670.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 2665-2670
    • Hu, Z.S.1    Mingarelli, A.B.2
  • 20
    • 0001757843 scopus 로고
    • Periodic and almost periodic solutions of Volterra integral differential equations with infinite memory
    • C. Langenhop, Periodic and almost periodic solutions of Volterra integral differential equations with infinite memory, J. Differential Equations, 58 (1985), 391-403.
    • (1985) J. Differential Equations , vol.58 , pp. 391-403
    • Langenhop, C.1
  • 21
    • 0003506615 scopus 로고
    • Almost Periodic Functions and Differential Equations
    • English translation by Cambridge Univ. Press, 1982
    • B. M. Levitan and V. V. Zhikov, Almost Periodic Functions and Differential Equations, Moscow Univ. Publ. House 1978, English translation by Cambridge Univ. Press, 1982.
    • (1978) Moscow Univ. Publ. House
    • Levitan, B.M.1    Zhikov, V.V.2
  • 22
    • 0001489955 scopus 로고    scopus 로고
    • A Massera type criterion for linear functional differential equations with advanced and delay
    • Y. Li, Z. Lin and Z. Li, A Massera type criterion for linear functional differential equations with advanced and delay, J. Math. Anal. Appl., 200 (1996), 715-725.
    • (1996) J. Math. Anal. Appl. , vol.200 , pp. 715-725
    • Li, Y.1    Lin, Z.2    Li, Z.3
  • 23
    • 0033131776 scopus 로고    scopus 로고
    • Periodic solutions for evolution equations
    • Y. Li, F. Cong, Z. Lin and W. Liu, Periodic solutions for evolution equations, Nonlinear Anal., 36(1999), 275-293.
    • (1999) Nonlinear Anal. , vol.36 , pp. 275-293
    • Li, Y.1    Cong, F.2    Lin, Z.3    Liu, W.4
  • 24
    • 84969034937 scopus 로고
    • The existence of periodic solutions of systems of differential equations
    • J. L. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J., 17 (1952), 457-475.
    • (1952) Duke Math. J. , vol.17 , pp. 457-475
    • Massera, J.L.1
  • 25
    • 0002978017 scopus 로고    scopus 로고
    • Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
    • S. Murakami, T. Naito and N. V. Minh, Evolution semigroups and sums of commuting operators: a new approach to the admissibility theory of function spaces, J. Differential Equations, 164 (2000), 240-285.
    • (2000) J. Differential Equations , vol.164 , pp. 240-285
    • Murakami, S.1    Naito, T.2    Minh, N.V.3
  • 26
    • 0033095590 scopus 로고    scopus 로고
    • Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations
    • T. Naito and N. V. Minh, Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations, J. Differential Equations, 152 (1999), 358-376.
    • (1999) J. Differential Equations , vol.152 , pp. 358-376
    • Naito, T.1    Minh, N.V.2
  • 27
    • 0033637878 scopus 로고    scopus 로고
    • A decomposition theorem for bounded solutions and the existence of periodic solutions to periodic differential equations
    • T. Naito, N. V. Minh, R. Miyazaki and J. S. Shin, A decomposition theorem for bounded solutions and the existence of periodic solutions to periodic differential equations, J. Differential Equations, 160 (2000), 263-282.
    • (2000) J. Differential Equations , vol.160 , pp. 263-282
    • Naito, T.1    Minh, N.V.2    Miyazaki, R.3    Shin, J.S.4
  • 29
    • 0035661223 scopus 로고    scopus 로고
    • New spectral criteria for almost periodic solutions of evolution equations
    • T. Naito, N. V. Minh and J. S. Shin, New spectral criteria for almost periodic solutions of evolution equations, Studia Math., 145 (2001), 97-111.
    • (2001) Studia Math. , vol.145 , pp. 97-111
    • Naito, T.1    Minh, N.V.2    Shin, J.S.3
  • 31
    • 0001459058 scopus 로고    scopus 로고
    • Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
    • N. V. Minh, F. Rabiger and R. Schnaubelt, Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line, Integral Equations Operator Theory, 32 (1998), 332-353.
    • (1998) Integral Equations Operator Theory , vol.32 , pp. 332-353
    • Minh, N.V.1    Rabiger, F.2    Schnaubelt, R.3
  • 32
    • 0003316678 scopus 로고
    • Semigroups of Linear Operators and Applications to Partial Differential Equations
    • Spriger-Verlag, Berlin-New York
    • A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Spriger-Verlag, Berlin-New York, 1983.
    • (1983) Appl. Math. Sci. , pp. 44
    • Pazy, A.1
  • 34
    • 0003683673 scopus 로고
    • Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity
    • W. M. Ruess and W. H. Summers, Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity, Dissertationes Math. (Rozprawy Mat.), 279 (1989).
    • (1989) Dissertationes Math. (Rozprawy Mat.) , pp. 279
    • Ruess, W.M.1    Summers, W.H.2
  • 35
    • 0000392619 scopus 로고
    • Asymptotically almost periodic solutions of evolution equations in Banach spaces
    • W. M. Ruess and Q. P. Vu, Asymptotically almost periodic solutions of evolution equations in Banach spaces, J. Differential Equations, 122 (1995), 282-301.
    • (1995) J. Differential Equations , vol.122 , pp. 282-301
    • Ruess, W.M.1    Vu, Q.P.2
  • 36
    • 84972545996 scopus 로고
    • Almost periodic solutions of Volterra equations
    • Q. P. Vu, Almost periodic solutions of Volterra equations, Differential Integral Equations, 7 (1994), 1083-1093.
    • (1994) Differential Integral Equations , vol.7 , pp. 1083-1093
    • Vu, Q.P.1
  • 37
    • 0001134447 scopus 로고    scopus 로고
    • The operator equation AX-XB = C, stability and asymptotic behaviour of differential equations
    • Q. P. Vu and E. Schiller, The operator equation AX-XB = C, stability and asymptotic behaviour of differential equations, J. Differential Equations, 145 (1998), 394-419.
    • (1998) J. Differential Equations , vol.145 , pp. 394-419
    • Vu, Q.P.1    Schiller, E.2
  • 38
    • 0033541221 scopus 로고    scopus 로고
    • Semi-Fredholm operators and periodic solutions for linear functional differential equations
    • J. S. Shin and T. Naito, Semi-Fredholm operators and periodic solutions for linear functional differential equations, J. Differential Equations, 153 (1999), 407-441.
    • (1999) J. Differential Equations , vol.153 , pp. 407-441
    • Shin, J.S.1    Naito, T.2
  • 39
    • 1842800115 scopus 로고    scopus 로고
    • Existence and uniqueness of periodic solutions to periodic linear functional differential equations with finite delay
    • J. S. Shin, T. Naito and N. V. Minh, Existence and uniqueness of periodic solutions to periodic linear functional differential equations with finite delay, Funkcial. Ekvac., 44 (2001), 53-71.
    • (2001) Funkcial. Ekvac. , vol.44 , pp. 53-71
    • Shin, J.S.1    Naito, T.2    Minh, N.V.3
  • 40
    • 0003587797 scopus 로고    scopus 로고
    • Theory and Applications of Partial Functional Differential Equations
    • Springer, Berlin-New York
    • J. Wu, Theory and Applications of Partial Functional Differential Equations, Appl. Math. Sci., 119, Springer, Berlin-New York, 1996.
    • (1996) Appl. Math. Sci. , pp. 119
    • Wu, J.1
  • 41
    • 0003462755 scopus 로고
    • Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions
    • Springer-Verlag, New York
    • T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Appl. Math. Sci., 14, Springer-Verlag, New York, 1975.
    • (1975) Appl. Math. Sci. , pp. 14
    • Yoshizawa, T.1


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