On periodic solutions of liénard type equations


The Liénard type equation x'' + f(x, x')x' + g(x) = 0 (i) is considered. We claim that if the associated conservative equation x'' + g(x) = 0 has period annuli then a dissipation f(x, x') exists such that a limit cycle of equation (i) exists in a selected period annulus. Moreover, it is possible to define f(x, x') so that limit cycles appear in all period annuli. Examples are given. A particular example presents two limit cycles of non-convex shape in two disjoint period annuli.

Keyword : multiple solutions, second-order equation, periodic solutions, limit cycles

How to Cite
Atslega, S., & Sadyrbaev, F. (2013). On periodic solutions of liénard type equations. Mathematical Modelling and Analysis, 18(5), 708-716.
Published in Issue
Dec 1, 2013
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