A continuation theorem with applications to periodically forced Liénard equations in the presence of a separatrix |
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| Authors: | Gabriele Villari Fabio Zanolin |
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| Institution: | (1) Dipartimento di Matematica “U. Dini”, Università, viale Morgagni 67/A, 50137 Firenze, e-mail: villari@udini.math.unifi.it, IT;(2) Dipartimento di Matematica e Informatica, Università, via delle Scienze 206, 33100 Udine, e-mail: zanolin@dimi.uniud.it , IT |
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| 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.
Received: April 27, 2000 Published online: December 19, 2001 |
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| Keywords: | : Liénard equation – periodic solutions – continuation methods |
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