Some explicit oscillation results for the generalised Liénard type systems

Abstract

In this work a generalised Lienard type system will be considered. We study the problem whether all trajectories of this system intersect the vertical isocline, which is very important in the global asymptotic stability of the origin, oscillation theory, and existence of periodic solutions. Under quite general assumptions we obtain sufficient conditions which are very sharp. We present some new conditions under which the solutions of this system are oscillatory. Some examples are provided to illustrate our results.