Continua of Periodic Solutions of the Liénard Equation
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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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