The existence of limit cycles of nonlinear oscillation equations (Q910906)

Many mathematicians have done a lot of work on the existence of limit cycles of the Lienard equation \(x''+f(x)x'+g(x)=0,\) and many good results have been obtained. It is worthwhile to generalize these results to more general nonlinear equation \[ (1)\quad x''+f(x)\eta (x')x'+\psi (x')g(x)=0. \] In this paper we use a new method to deal with the existence of limit cycles of the equation (1) and obtain some new results. Our results generalize the well-known theorems of Dragilev and Filippov.