On the existence and uniqueness of limit cycles in Lienard differential equations allowing discontinuities

In this paper we study the non-existence and the uniqueness of limit cycles for the Lienard differential equation of the form x '' - f (x) x ' + g(x) = 0 where the functions f and g satisfy xf (x) > 0 and xg(x) > 0 for x not equal 0 but can be discontinuous at x = 0. In particular, our results allow us to prove the non-existence of limit cycles under suitable assumptions, and also prove the existence and uniqueness of a limit cycle in a class of discontinuous Lienard systems which are relevant in engineering applications.