On periodic solutions of liénard type equations

    Svetlana Atslega Info
    Felix Sadyrbaev Info

Abstract

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.

Keywords:

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. https://doi.org/10.3846/13926292.2013.871651

Share

Published in Issue
December 1, 2013
Abstract Views
657

View article in other formats

CrossMark check

CrossMark logo

Published

2013-12-01

Issue

Section

Articles

How to Cite

Atslega, S., & Sadyrbaev, F. (2013). On periodic solutions of liénard type equations. Mathematical Modelling and Analysis, 18(5), 708-716. https://doi.org/10.3846/13926292.2013.871651

Share