On Periodic Solutions of Liénard Type Equations

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

AMS Subject Classification:

• 34B08
• 34B15