Continuability and (non-) oscillatory properties of solutions of generalized Liénard equation (Q749732)

The paper deals with the equation (1) \(x''+f(x)x'+g(x)=0\) where f and g are continuous on R and \(xf(x)>0\), \(xg(x)>0\) for all \(x\neq 0\). There are treated the problems of continuability of the solutions, the properties of (ultimately) positive and negative solutions, the nonexistence of such solutions and consequently there are stated sufficient conditions for the oscillation of all solutions existing in a neighbourhood of \(t=\infty\). The problem of the existence of ultimately positive (negtive) solutions of (1) will be discussed in the papers which are prepared to be published.