A note on existence and uniqueness of limit cycles for Liénard systems

Journal of Mathematical Analysis and Applications

Volumn 307, Issue 2, 2005, Pages 763-773

  Carletti, Timoteo ^a   Villari, Gabriele ^b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b Dipartimento di Matematica U Dini   (Italy)

Author keywords

Existence and uniqueness; Li nard equation; Limit cycles

Indexed keywords

EID: 18944386717     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.01.054     Document Type: Article

References (15)

1. T. Carletti, Uniqueness of limit cycles for a class of planar vector fields, QTDS (2005), in press
2. G.F.D. Duff N. Levinson On the non-uniqueness of periodic solutions for an asymmetric Liénard equation Quart. Appl. Math. 10 1952 86-88
3. A.F. Filippov A sufficient condition for the existence of a stable limit cycle for a second order equation Mat. Sb. 30 1952 171-180
4. N. Levinson O.K. Smith A general equation for relation oscillations Duke Math. J. 9 1942 382-403
5. J.L. Massera Sur un théorème de G. Sansone sur l'équation de Liénard Boll. Un. Mat. Ital. 9 1954 367-369
6. M. Sabatini, G. Villari, About limit cycle's uniqueness for a class of generalized Liénard systems, preprint number 672, Univ. Trento, 2004
7. G. Sansone Sopra l'equazione di A. Liénard delle oscillazioni di rilassamento Ann. Mat. Pura Appl. (4) 28 1949 153-181
8. H. Serbin Periodic motions of non-linear dynamical system Quart. Appl. Math. 8-A 1950 296-303
9. U. Staude Uniqueness of periodic solutions of the Liénard equation Recent Advances in Differential Equations 1981 Academic Press 421-429
10. G. Villari On the existence of periodic solutions for Liénard equation Nonlinear Anal. 7 1983 71-78
11. G. Villari Some remarks on the uniqueness of the periodic solutions for Liénard's equation Boll. Unione Mat. Ital., Anal. Funz. Appl. C (6) IV 1985 173-182
12. G. Villari On the qualitative behaviour of solutions of Liénard equation J. Differential Equations 67 1987 269-277
13. D. Xiao Z. Zhang On the uniqueness and nonexistence of limit cycles for predator-prey systems Nonlinearity 16 2003 1185-1201
14. Y.Q. Ye et al. Theory of Limit Cycles Transl. Math. Monogr. vol. 66 1986 Amer. Math. Soc. Providence, RI
15. Z. Zhi-fen et al. Qualitative Theory of Differential Equations Transl. Math. Monogr. vol. 101 1992 Amer. Math. Soc. Providence, RI