Applied Mathematics and Mechanics

, Volume 18, Issue 12, pp 1205–1210 | Cite as

A necessary and sufficient condition for the oscillation of solutions of Liénard type system with multiple singular points

  • Sun Jitao
  • Zhang Yinping


In this paper, a necessary and sufficient condition for the solution of Liénard type system with multiple singular points to oscillation under the more general assumption is given. Results of the papers [1∼4] are also extended and improved in this paper.

Key words

Liénard type system oscillating solution necessary and sufficient condition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. R., Graef, On the Generalized Liénard equation with negative damping.J. Diff. Eqs.,12 (1972), 34–62.Google Scholar
  2. [2]
    G., Villari, On the qualitative behaviour of solutions of Liénard equation,J. Diff. Eqs.,67 (1987), 269–27.Google Scholar
  3. [3]
    Han, Maoan, Periodic solution, unbounded solution and oscillation solution about equationx=ϕ(y) − F(x), y=−g(x),J. Nanjing University Mathematical Biquarterly,1 (1984), 89–101. (in Chinese)Google Scholar
  4. [4]
    Sun, Jitao, On sufficient and necessary condition of solution to oscillate abount systemx=h(y) − F(x), y=−g(x),J, Nanjing University Mathematical Biquartevly,9 (1992), 113–119. (in Chinese)Google Scholar
  5. [5]
    Lin, Jibin, A class of limit cycle distribution of plane cubic system,Scientia Sinica (Series A),7 (1984), 586–596. (in Chinese)Google Scholar
  6. [6]
    A., Sandquist and K. M., Andersen, A necessary and sufficient condition for the existence of unique nontrivial periodic solution to a class of equations of Liénard type,J. Diff. Eqs.,46 (1982), 356–378.Google Scholar
  7. [7]
    Wang, Xian, Some remarks on the limit cycle for equation of Liénard type,Chin. Quar. J. Math.,5 (1990), 122–130. (in Chinese)Google Scholar
  8. [8]
    Sun, Jiato. On the boundedness of solutions and existence of limit cycle of Liénard type equation,Appl. Math. J. Chinese Univ. Ser. A,7 (1992), 184–191. (in Chinese)Google Scholar
  9. [9]
    Han, Maoan, Global property of diffrential equation with multiple singular points.Acta Mathematica Scientia,33 (1990), 684–693. (in Chinese)Google Scholar
  10. [10]
    Sun, Jitao, On the qualitative behaviour of solution of generalized Lienard equation.Acta Mathematica Scientia,14 (1994), 90–95, (in Chinese)Google Scholar
  11. [11]
    T., Hara and T., Yoneyama, On the global center of generalized Liénard equation and its application to stability problems,Funkical. Ekvac.,28 (1985), 171–192.Google Scholar
  12. [12]
    G., Villari and F., Zanolin, On a dynamical system in the Liénard plane, necessary and sufficient conditions for the intersection with the vertical isocline and applications,Funkical. Ekvac.,33 (1990), 19–38.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Sun Jitao
    • 1
  • Zhang Yinping
    • 1
  1. 1.Shanghai Tiedao UniversityShanghaiP. R. China

Personalised recommendations