Abstract
Some conditions for the existence, non-uniqueness or uniqueness and iterative construction of periodic solutions of the non-autonomous Liénard equation are considered. Especially, the problem of continua of oscillations is discussed, under conditions suggested by Bebernes-Martelli. It is shown that all periodic solutions result from one by adding a constant, and that the restoring term must be of a special degenerate type. If this term is not explicitly depending on the time an existence and uniqueness theorem can be formulated.
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© 1979 Springer Basel AG
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Reißig, R. (1979). Continua of Periodic Solutions of the Liénard Equation. In: Albrecht, J., Collatz, L., Kirchgässner, K. (eds) Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Serie Internationale D’Analyse Numerique, vol 48. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6283-7_9
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DOI: https://doi.org/10.1007/978-3-0348-6283-7_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1098-1
Online ISBN: 978-3-0348-6283-7
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