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Oscillation of solutions of a generalized Liénard equation

The generalized Lienard equation, . +f(x, x) + h(x)=O, with xh(x)>O and yf(x,y)>O for nonzero x and y, is considered here, subject to the additional condition that If(x,y)l is not greater than k(x) IyIa where oc is a positive number and k(x) is a continuous function which is positive for nonzero x. In case oc>2, all solutions of this Lienard equation are oscillatory. In case O<oc<2, sufficient conditions are given which insure that all solutions are oscillatory.