On the structure of the set of bounded solutions on a periodic Liénard equation
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- by Juan Campos and Pedro J. Torres PDF
- Proc. Amer. Math. Soc. 127 (1999), 1453-1462 Request permission
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.References
- M. Brown, Homeomorphisms of two-dimensional manifolds, Houston J. Math. 11 (1985), no. 4, 455–469. MR 837985
- 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.
- Patrick Habets and Luis Sanchez, Periodic solutions of some Liénard equations with singularities, Proc. Amer. Math. Soc. 109 (1990), no. 4, 1035–1044. MR 1009991, DOI 10.1090/S0002-9939-1990-1009991-5
- A. C. Lazer and S. Solimini, On periodic solutions of nonlinear differential equations with singularities, Proc. Amer. Math. Soc. 99 (1987), no. 1, 109–114. MR 866438, DOI 10.1090/S0002-9939-1987-0866438-7
- Pedro Martínez-Amores and Pedro J. Torres, Dynamics of a periodic differential equation with a singular nonlinearity of attractive type, J. Math. Anal. Appl. 202 (1996), no. 3, 1027–1039. MR 1408365, DOI 10.1006/jmaa.1996.0358
- Rafael Ortega, Periodic solutions of a Newtonian equation: stability by the third approximation, J. Differential Equations 128 (1996), no. 2, 491–518. MR 1398329, DOI 10.1006/jdeq.1996.0103
- Russell A. Smith, Massera’s convergence theorem for periodic nonlinear differential equations, J. Math. Anal. Appl. 120 (1986), no. 2, 679–708. MR 864784, DOI 10.1016/0022-247X(86)90189-7
- Amine Zitan and Rafael Ortega, Existence of asymptotically stable periodic solutions of a forced equation of Liénard type, Nonlinear Anal. 22 (1994), no. 8, 993–1003. MR 1277595, DOI 10.1016/0362-546X(94)90062-0
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
- MR Author ID: 610924
- ORCID: 0000-0002-1243-7440
- Email: ptorres@goliat.ugr.es
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1625713