Article PDF
Avoid common mistakes on your manuscript.
References
T. A. Burton,The generalized Liénard equation, SLAM J. Control Ser. A,3 (1965), pp. 223–230.
T. A. Burton,Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, Orlando, Florida (1985).
T. A. Burton -L. Hatvani,Stability theorems for nonautonomous functional differential equations by Liapunov functionals, Tôhoku Math. J.,41 (1989), pp. 65–104.
T. A. Burton -C. G. Townsend,On the generalized Liénard equation with forcing function, J. Diff. Eq.,4 (1968), pp. 620–633.
T. A. Burton -Bo Zhang,Uniform ultimate boundedness and periodicity in functional differential equations, Tôhoku Math. J.,42 (1990), pp. 93–100.
J. R. Graef,On the generalized Liénard equation with negative damping, J. Diff. Eq.,12 (1972), pp. 34–62.
J. K. Hale -O. Lopes,Fixed point theorems and dissipative processes, J. Diff. Eq.,13 (1973), pp. 391–402.
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.
N. N. Krasovskii,Stability of Motion, Stanford University Press, Stanford, California (1963).
S. Murakami,Asymptotic behavior of solutions of some differential equations, J. Math. Anal. Appl.,109 (1985), pp. 534–545.
G. Sansone -R. Conti,Non-linear Differential Equations, MacMillan, New York (1964).
A. Somolinos,Periodic solutions of the sunflower equation, Quart. Appl. Math.,35 (1978), pp. 465–478.
J. Sugie,On the generalized Liénard equation without the Signum condition, J. Math. Anal. Appl.,128 (1987), pp. 80–91.
J. Sugie,On the boundedness of solutions of the generalized Liénard equation without the Signum condition, Nonlinear Analysis,11 (1987), pp. 1391–1397.
G. Villari,On the qualitative behaviour of solutions of Liénard equation, J. Diff. Eq.,67 (1987), pp. 269–277.
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.
P. Waltman -T. F. Bridgland,On convergence of solutions of the forced Liénard equation, J. Math. Phys.,44 (1965), pp. 284–287.
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.
BoZhang,On the retarded Liénard equation, Proc. Amer. Math. Soc., in press.
Author information
Authors and Affiliations
Additional information
This research was supported in part by a Fulbright grant with number 9041635.
On leave from Northeast Normal University, Changchun, Jilin, P.R. China.
Rights and permissions
About this article
Cite this article
Burton, T.A., Zhang, B. Boundedness, periodicity, and convergence of solutions in a retarded liénard equation. Annali di Matematica pura ed applicata 165, 351–368 (1993). https://doi.org/10.1007/BF01765856
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01765856