|
Abstract
|
In this work a generalised Liénard 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.
|