The problem of uniqueness of limit cycles for the Liénard equation x¨+f(x)x˙+g(x) =0 is investigated. The classical assumption of sign-definiteness of f(x) is relaxed. The effectiveness of our result as a perturbation technique is illustrated by some constructive examples of small amplitude limit cycles, coming from bifurcation theory.
On the uniqueness of the limit cycle for the Liénard equation with f(x) not sign-definite / Gabriele Villari; Fabio Zanolin. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 76:(2018), pp. 208-2014. [10.1016/j.aml.2017.09.004]
On the uniqueness of the limit cycle for the Liénard equation with f(x) not sign-definite
VILLARI, GABRIELE;
2018
Abstract
The problem of uniqueness of limit cycles for the Liénard equation x¨+f(x)x˙+g(x) =0 is investigated. The classical assumption of sign-definiteness of f(x) is relaxed. The effectiveness of our result as a perturbation technique is illustrated by some constructive examples of small amplitude limit cycles, coming from bifurcation theory.
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