Abstract
We use classical Leray-Schauder techniques in order to derive the existence of periodic solutions of a generalized Liénard equation with delay.
Keywords
- Delay
- periodic solutions
- Caratheodory's conditions
Work performed under the auspices of "Gruppo Nazionale per l'Analisi Funzionale ed Applicazioni" — Italy.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.BEBERNES, M.MARTELLI-Periodic solutions for Liénard Systems, Atti Equadiff 78, Firenze, 537–545.
E.F. BECKENBACH, R. BELLMANN-"Inequalities" Springer Verlag, Berlin 1961.
J. CRONIN-Fixed points and topological degree in nonlinear analysis, Amer. Math. Soc., Providence, R.I., 1964.
J. HALE-Functional differential equations, Springer Verlag Berlin, 1971.
A. LASOTA, Z. OPIAL Sur les solutions périodiques des equations différentielles ordinaires, Ann. Pol. Math. 16 (1964) 69–94.
M. MARTELLI-On forced nonlinear oscillations, J.Math.Anal.Appl. 69, 1979, 496–504.
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 equations at resonance (to appear in Arch. Math.).
J.MAWHIN, J.R.WARD Jr.-Nonuniform nonresonance conditions at the two first eigenvalues for periodic solutions of forced Liénard and Duffing equations. (to appear in Rocky Mountains Math. J.-1982).
C.MIRANDA-Istituzioni di Analisi di Analisi Funzionale Lineare, Un.Mat.Ital., 1978.
R.REISSIG-Extension of some results concerning the generalized Liénard equation, Ann.Mat.Pura Appl., 1975, 269–281.
G. SANSONE, R. CONTI-Equazioni differenziali non lineari, Cremonese Roma, 1956.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
De Pascale, E., Iannacci, R. (1983). Periodic solutions of generalized Lienard equations with delay. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103246
Download citation
DOI: https://doi.org/10.1007/BFb0103246
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12686-7
Online ISBN: 978-3-540-38678-0
eBook Packages: Springer Book Archive
