Annali di Matematica Pura ed Applicata

, Volume 139, Issue 1, pp 313–327 | Cite as

Periodic solutions of Liénard systems at resonance

  • G. Conti
  • B. Iannacci
  • M. N. Nkashama
Article

Summary

We use classical Leray-Schauder techniques in order to derive the existence of periodic solutions for Liénard differential systems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Bebernes,A simple alternative problem for finding periodic solutions of second order ordinary differential equations, Proc. Amer. Math. Soc.,48 (1974), pp. 121–127.Google Scholar
  2. [2]
    J. Bebernes -M. Martelli,Periodic solutions for Liénard systems, Boll. Un. Mat. Ital., (5)16-A (1979), pp. 398–405.Google Scholar
  3. [3]
    L. Cesari -R. Kannan,Solutions in the large of Liénard systems with forcing terms, Ann. Mat. Pura Appl., (4)111 (1976), pp. 101–124.Google Scholar
  4. [4]
    L. Cesari -R. Kannan,Periodic solutions in the large of Liénard systems with forcing terms, Boll. Un. Mat. Ital., (6)1-A (1982), pp. 217–223.Google Scholar
  5. [5]
    S. H. Chang,Periodic solutions of certain second order nonlinear differential equations, J. Math. Anal. Appl.,49 (1975), pp. 263–266.Google Scholar
  6. [6]
    J. Cronin,Fixed Points and Topological Degree in Nonlinear Analysis, Math. Survey No. 11, Amer. Math. Soc., Providence, R.I., 1964.Google Scholar
  7. [7]
    C. P.Gupta - J.Mawhin,Asymptotic conditions at the two first eigenvalues for the periodic solutions of Liénard differential equations and an inequality of E. Schmidt, Rapport n. 10 Sem. Math., (1982), Université Catholique de Louvain.Google Scholar
  8. [8]
    A. C. Lazer,On Schauder's fixed point theorem and forced second order nonlinear oscillations, J. Math. Anal. Appl.,81 (1968), pp. 421–425.Google Scholar
  9. [9]
    M. Martelli,On forced nonlinear oscillations, J. Math. Anal. Appl.,69 (1979), pp. 456–504.Google Scholar
  10. [10]
    M. Martelli -J. D. Schuur,Periodic solutions of Liénard type second order ordinary differential equations, Tohoku Math. J.,38 (1980), pp. 201–207.Google Scholar
  11. [11]
    J. Mawhin,An extension of a theorem of A.C. Laser on forced nonlinear equations, J. Math. Anal. Appl.,40 (1972), pp. 20–29.Google Scholar
  12. [12]
    J.Mawhin - J. R.Ward,Periodic solutions of some forced Liénard differential equations at resonance, to appear.Google Scholar
  13. [13]
    R. Reissig,Schwingungssätze für die verallgemeinerte Liénardsche Differentialgleichung, Abh. Math. Seminar Univ. Hamburg,44 (1975), pp. 45–51.Google Scholar
  14. [14]
    R. Reissig,Continua of periodic solutions of the Liénard equation, in « Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations », I.S.N.M., vol. 48, Birkhàuser, Basel, (1979), pp. 126–133.Google Scholar
  15. [15]
    R. Reissig,Uber einen allgemeinen Typ erzwungener nichtlinearer Schwingungen zweiter Ordnung, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.,56 (1974), pp. 297–302.Google Scholar
  16. [16]
    R. Reissig,Extension of some results concerning the generalized Liénard equations, Ann. Mat. Pura Appl.,104 (1975), pp. 269–281.Google Scholar
  17. [17]
    R. Reissig,Contractive mappings and periodically perturbed nonconservative systems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat.,52 (1975), pp. 698–702.Google Scholar
  18. [18]
    N. Rouche -J. Mawhin,Equations differentielles ordinaires (2 Volumes), Masson, Paris, 1972.Google Scholar
  19. [19]
    P. Zanolin,Remark on Multiple Periodic Solutions for Nonlinear Ordinary Differential Systems of Liénard Type, Boll. Un. Mat. Ital., (6)1-B (1982), pp. 683–698.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1985

Authors and Affiliations

  • G. Conti
    • 1
  • B. Iannacci
    • 2
  • M. N. Nkashama
    • 3
  1. 1.Firenze
  2. 2.Cosenza
  3. 3.LouvainBelgium

Personalised recommendations