Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations
In this paper, we consider one--parameter ($λ>0$) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of $λ>0$. To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of $λ$ and the second one for small values of $λ$. In particular, our hypotheses allow us to establish a link between these two theories.
math.DS↗