On the structure of the set of bounded solutions on a periodic Liénard equation

Authors:
Juan Campos and Pedro J. Torres

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1453-1462

MSC (1991):
Primary 34C25, 54H20

DOI:
https://doi.org/10.1090/S0002-9939-99-05046-7

Published electronically:
January 29, 1999

MathSciNet review:
1625713

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Abstract | References | Similar Articles | Additional Information

Abstract: We describe the dynamics of a class of second order periodic differential equations whose main feature is a monotone nonlinearity. It is proved that the set of bounded solutions is homeomorphic to the graph of a decreasing function.

**1.**M. BROWN, Homeomorphisms of two-dimensional manifolds,*Houston J. of Math.*,**11**, (1985), 455-469. MR**87g:57020****2.**J. CAMPOS; R. ORTEGA; A. TINEO , Homeomorphisms of the disk with trivial dynamics and extinction of competitive systems,*J. Diff. Equ.***138**, (1997), 157-170. CMP**97:15****3.**P. HABETS; L. SANCHEZ , Periodic solutions of some Liénard equations with singularities,*Proc. Amer. Math. Soc.*,**109**, (1990), 1035-1044. MR**90k:34049****4.**A.C. LAZER; S. SOLIMINI, On periodic solutions of nonlinear differential equations with singularities,*Proc. Amer. Math. Soc.*,**99**, (1987), 109-114. MR**87k:34064****5.**P. MART[??]NEZ-AMORES; P. J. TORRES, Dynamics of a periodic differential equation with a singular nonlinearity of attractive type,*J. Math. Anal. and Appl.*,**202**, (1996), 1027-1039. MR**97f:34027****6.**R. ORTEGA, Periodic Solutions of a Newtonian Equation: Stability by the Third Approximation,*J. Diff. Equ.*,**128**, (1996), 491-518. MR**97m:34077****7.**R.A. SMITH, Massera's convergence theorem for periodic nonlinear differential equations,*J. Math. Anal. and Appl.*,**120**, (1986), 679-708. MR**87k:34068****8.**A. ZITAN; R. ORTEGA, Existence of asymptotically stable periodic solutions of a forced equation of Liénard type,*Nonlinear Anal.*,**22**, (1994), 993-1003. MR**95f:34047**

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Additional Information

**Juan Campos**

Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain

Email:
jcampos@goliat.ugr.es

**Pedro J. Torres**

Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain

Email:
ptorres@goliat.ugr.es

DOI:
https://doi.org/10.1090/S0002-9939-99-05046-7

Received by editor(s):
August 31, 1997

Published electronically:
January 29, 1999

Additional Notes:
This work was supported by D.G.E.S. PB95-1203, M.E.C., Spain, and E.E.C. project ERBCHRX-CT94-0555

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1999
American Mathematical Society