An extension of Dragilev’s theorem for the existence of periodic solutions of the Liénard equation

The problem of the existence of periodic solution for the Liénard equation is investigated, and a result which improves the classical Dragilev’s theorem is presented, together with a corollary in which there are no assumptions on the function g(x)g(x), and hence on G(x)G(x), besides the standard sign condition. In the final part of the paper constructive examples with several limit cycles are provided.