Annali di Matematica Pura ed Applicata

, Volume 165, Issue 1, pp 351–368 | Cite as

Boundedness, periodicity, and convergence of solutions in a retarded liénard equation

  • T. A. Burton
  • Bo Zhang


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  1. [1]
    T. A. Burton,The generalized Liénard equation, SLAM J. Control Ser. A,3 (1965), pp. 223–230.Google Scholar
  2. [2]
    T. A. Burton,Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, Orlando, Florida (1985).Google Scholar
  3. [3]
    T. A. Burton -L. Hatvani,Stability theorems for nonautonomous functional differential equations by Liapunov functionals, Tôhoku Math. J.,41 (1989), pp. 65–104.Google Scholar
  4. [4]
    T. A. Burton -C. G. Townsend,On the generalized Liénard equation with forcing function, J. Diff. Eq.,4 (1968), pp. 620–633.Google Scholar
  5. [5]
    T. A. Burton -Bo Zhang,Uniform ultimate boundedness and periodicity in functional differential equations, Tôhoku Math. J.,42 (1990), pp. 93–100.Google Scholar
  6. [6]
    J. R. Graef,On the generalized Liénard equation with negative damping, J. Diff. Eq.,12 (1972), pp. 34–62.Google Scholar
  7. [7]
    J. K. Hale -O. Lopes,Fixed point theorems and dissipative processes, J. Diff. Eq.,13 (1973), pp. 391–402.Google Scholar
  8. [8]
    T. Hara -T. Yoneyama,On the global center of generalized Liénard equation and its application to stability problems, Funkeialaj Ekvacioj,28 (1985), pp. 171–192.Google Scholar
  9. [9]
    N. N. Krasovskii,Stability of Motion, Stanford University Press, Stanford, California (1963).Google Scholar
  10. [10]
    S. Murakami,Asymptotic behavior of solutions of some differential equations, J. Math. Anal. Appl.,109 (1985), pp. 534–545.Google Scholar
  11. [11]
    G. Sansone -R. Conti,Non-linear Differential Equations, MacMillan, New York (1964).Google Scholar
  12. [12]
    A. Somolinos,Periodic solutions of the sunflower equation, Quart. Appl. Math.,35 (1978), pp. 465–478.Google Scholar
  13. [13]
    J. Sugie,On the generalized Liénard equation without the Signum condition, J. Math. Anal. Appl.,128 (1987), pp. 80–91.Google Scholar
  14. [14]
    J. Sugie,On the boundedness of solutions of the generalized Liénard equation without the Signum condition, Nonlinear Analysis,11 (1987), pp. 1391–1397.Google Scholar
  15. [15]
    G. Villari,On the qualitative behaviour of solutions of Liénard equation, J. Diff. Eq.,67 (1987), pp. 269–277.Google Scholar
  16. [16]
    G. Villari -F. Zanolin,On a dynamical system in the Liénard plane. Necessary and sufficient conditions for the intersection with the vertical isocline and application, Funcialaj Ekvacioj,33 (1990), pp. 19–38.Google Scholar
  17. [17]
    P. Waltman -T. F. Bridgland,On convergence of solutions of the forced Liénard equation, J. Math. Phys.,44 (1965), pp. 284–287.Google Scholar
  18. [18]
    T. Yoshizawa,Asymptotic behavior of solutions of differential equations, inDifferential Equations qualitative Theory (Szeged, 1984), Colloq. Math. Soc. János Bolyai,47, North-Holland, Amsterdam (1984), pp. 1141–1172.Google Scholar
  19. [19]
    BoZhang,On the retarded Liénard equation, Proc. Amer. Math. Soc., in press.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1993

Authors and Affiliations

  • T. A. Burton
    • 1
  • Bo Zhang
    • 1
  1. 1.Department of MathematicsSouthern Illinois University at CarbondaleCarbondale

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