The problem of uniqueness of limit cycles for the Lienard equation is investigated. Some sucient conditions are presented which complement recent related results. The proofs are based on an energy level comparison method which guarantees that all the possible limit cycles intersect the lines x = a and x = b; being a < 0 < b the two nontrivial zeros of F(x): Some examples illustrate the range of applicability of the main results. Keywords: Liénard equation, Limit cycles, Uniqueness. MSC classification: 34C05, 34C25, 34C15.
On the uniqueness of the limit cycle for the Liénard equation, via comparison method for the energy level curves / Gabriele, Villari; Fabio, Zanolin. - In: DYNAMIC SYSTEMS AND APPLICATIONS. - ISSN 1056-2176. - STAMPA. - 25:(2016), pp. 321-334.
On the uniqueness of the limit cycle for the Liénard equation, via comparison method for the energy level curves
VILLARI, GABRIELE;
2016
Abstract
The problem of uniqueness of limit cycles for the Lienard equation is investigated. Some sucient conditions are presented which complement recent related results. The proofs are based on an energy level comparison method which guarantees that all the possible limit cycles intersect the lines x = a and x = b; being a < 0 < b the two nontrivial zeros of F(x): Some examples illustrate the range of applicability of the main results. Keywords: Liénard equation, Limit cycles, Uniqueness. MSC classification: 34C05, 34C25, 34C15.
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