Necessary and sufficient conditions for boundedness and oscillation in the retarded Liénard equation

Journal of Mathematical Analysis and Applications

Volumn 200, Issue 2, 1996, Pages 453-473

  Zhang, Bo ^a  

^a FAYETTEVILLE STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030162786     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0216     Document Type: Article

References (17)

1. 1. T. A. Burton, On the generalized Liénard equation, SIAM J. Control Optim. 3 (1965), 223-230.
2. 2. T. A. Burton and C. G. Townsend, On the generalized Liénard equation with forcing function, J. Differential Equations 4 (1968), 620-633.
3. 3. T. A. Burton, "Stability and Periodic Solutions of Ordinary and Functional Differential Equations," Academic Press, Orlando, FL, 1985.
4. 4. J. R. Graef, On the generalized Liénard equation with negative damping, J. Differential Equations 12 (1972), 34-62.
5. 5. J. K. Hale, "Theory of Functional Differential Equations," Springer-Verlag, New York, 1977.
6. 6. T. Hara, T. Yoneyama, and J. Sugie, A necessary and sufficient condition for oscillation of the generalized Liénard equation, Ann. Mat. Pura Appl. 154 (1989), 223-230.
7. 7. N. N. Krasovskii, "Stability of Motion," Stanford Univ. Press, Stanford, CA, 1963.
8. 8. S. Murakami, Asymptotic behavior of solutions of some differential equations, J. Math. Anal. Appl. 109 (1985), 534-545.
9. 9. S. B. Norkin, "Differential Equations of the Second Order with Retarded Argument," Translations of Mathematical Monographs, Vol. 30, Amer. Math. Soc. Providence, RI, 1972.
10. 10. A. Sansoné and R. Conti, "Nonlinear Differential Equations," Macmillan Co., New York, 1964.
11. 11. A. Somolinos, Periodic solutions of the sunflower equation, Quart. Appl. Math. 109 (1985), 534-545.
12. 12. J. Sugie, On the boundedness of solutions of the generalized Liénard equation without the signum condition, Nonlinear Anal. 11 (1987), 1391-1397.
13. 13. G. Villari, On the qualitative behavior of solutions of the Liénard equation, J. Differential Equations 67 (1987), 267-277.
14. 14. G. Villari and F. Zanolin, On a dynamical system in the Liénard plane, Necessary and sufficient conditions for the intersections with the vertical isociline and application, Funkcial. Ekvac. 33 (1990), 19-38.
15. 15. B. Zhang, On the retarded Liénard equation, Proc. Amer. Math. Soc. 115 (1992), 779-785.
16. 16. B. Zhang, Boundedness and stability of solutions of the retarded Liénard equation with negative damping, Nonlinear Anal. 20 (1993), 303-313.
17. 17. T. Yoshizaw, Asymptotic behavior of solutions of differential equations, in "Differential Equations: Qualitative Theory (Szeged, 1984)," pp. 1141-1172, Colloq. Math. Soc. János Bolyai, Vol. 47, North-Holland, Amsterdam, 1987.