references
L. Cesari, R. Kannan, Periodic solutions in the large of Liénard systems with forcing terms, Boll. Un. Mat. Ital. A (6) 1 (1982), 217–224.
E.N. Dancer, On the ranges of certain damped nonlinear differential equations, Ann. Mat. Pura Appl. (4) 119 (1979), 281–295.
M.LC. Fernandes, F. Zanolin, Periodic solutions of a second order differential equation with one-sided growth restrictions on the restoring term, Arch. Math, (to appear).
J.R. Graef, On the generalized Liénard equation with negative damping, J. Differential Equations 12 (1972), 34–62.
T. Hara, T. Yoneyama, Necessary an sufficient conditions for the continuability of solutions of the system x′=y−F(x), y′=−g(x), Applicable Anal. 19 (1985), 169–180.
R. Iannacci, M.N. Nkashama, P. Omari, F. Zanolin, Periodic solutions of forced Liénard equations with jumping nonlinearities under nonuniform conditions, preprint (1987).
S. Invernizzi, F. Zanolin, Periodic solutions of a differential delay equation of Rayleigh type, Rend. Sem. Mat Univ. Padova 61 (1979), 115–124.
A.C. Lazer, On Schauder’s fixed point theorem and forced second order nonlinear oscillations, J. Math. Anal. Appl. 21 (1968), 421–425.
J. Mawhin, Dégré topologique et solutions périodiques des systèmes différentielles nonlinéaires, Bull. Soc. Roy. Sci. Liège 38 (1969), 308–398.
J. Mawhin, An extension of a theorem of A.C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl. 40 (1972), 20–29.
J. Mawhin, J.R. Ward Jr., Periodic solutions of some forced Liénard differential equations at resonance, Arch. Math. 41 (1983), 337–351.
P. Omari, Gab. Villari, F. Zanolin, Periodic solutions of the Liénard equation with one-sided growth restrictions, J. Differential Equations 67 (1987), 278–293.
P. Omari, Gab. Villari, F. Zanolin, A survey of recent applications of fixed point theory to periodic solutions of the Liénard equation, in “Fixed point theory and its applications” (R.F. Brown, Ed.), Amer. Math. Soc, Providence R. I., 1987 (in press).
R. Reissig, Extensions of some results concerning the generalized Liénard equation, Ann. Mat. Pura Appl. (4) 104 (1975), 269–281.
R. Reissig, Schwingungssatze für die verallgemeinerte Liénardsche Differentialgleichung, Abh. Math. Sem. Univ. Hamburg 44 (1975), 45–51.
R. Reissig, Periodic solutions of a second order differential equation including a one-sided restoring term, Arch. Math. 33 (1979), 85–90.
R.Reissig, G. Sansone, R. Conti, “Qualitative Theorie nichtlinearer Differentialgleichungen”, Edizioni Cremonese, Roma, 1963.
G. Sansone, R. Conti, “Equazioni differenziali non lineari”, Edizioni Cremonese, Roma, 1956.
Gab. Villari, F. Zanolin, On a dynamical system in the Liénard plane. Necessary and sufficient conditions for the intersection with the vertical isocline and applications, Funkc. Ekv. (to appear).
F. Zanolin, Periodic solutions for differential systems of Rayleigh type, Rend. 1st. Mat. Univ. Trieste 12 (1980), 69–77.
F. Zanolin, Periodic solutions for second order differential systems with damping, Rend. Sem. Mat. Univ. Padova 65 (1981), 223–234.
F. Zanolin, On forced nonlinear oscillations for some second order delay-differential systems, in “Evolution equations and their applications” (F. Kappel and W. Shappacher, Eds.), Researches Notes in Mathematics Vol. 68, pp. 295–313, Pitman, Boston, 1982.
Author information
Authors and Affiliations
Additional information
Dedicated to Prof. Dr. R. Reissig on the occasion of his 65th birthday.
Rights and permissions
About this article
Cite this article
Omari, P., Villari, G. On a continuation lemma for the study of a certain planar system with applications to liénard and rayleigh equations. Results. Math. 14, 156–173 (1988). https://doi.org/10.1007/BF03323223
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03323223