Abstract.
In this paper we prove a result on the existence of periodic motions for the periodically forced Liénard differential equation x ″+f(x)x ′+g(x)=e(t) in a situation where the phase portrait of the associated autonomous equation is similar to that of a centre limited by an unbounded separatrix. The existence result, which is based on a degree theoretic continuation theorem, enables us to treat some interesting cases not previously considered in the literature.
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Received: April 27, 2000 Published online: December 19, 2001
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Villari, G., Zanolin, F. A continuation theorem with applications to periodically forced Liénard equations in the presence of a separatrix. Ann. Mat. Pura Appl. IV. Ser. 180, 387–411 (2002). https://doi.org/10.1007/s102310100017
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DOI: https://doi.org/10.1007/s102310100017