|
Abstract
|
In this manuscript a generalized Li´enard system will be considered. First,
the existence and uniqueness of the solutions of the related initial value problem will be
proven. Given some definitions, a necessary and sufficient condition for property (Z+
1 )
will be presented. Some explicit conditions will also be given for the system to have
or fail to have properties (Z+
1 ). These results are very sharp and extend and improve
the previous results in this subject. Finally, a necessary and sufficient condition will
be presented about the existence and nonexistence of homoclinic orbits in the upper or
lower half-plane. At the end, some examples will be provided to illustrate our results.
|