TITLE:
Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems
AUTHORS:
Hongtao Zhang, Xiaolin Liu, Ping Yan
KEYWORDS:
Generalized Liénard System, Nonlinear Integral Inequality, Oscillation
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.6,
June
26,
2024
ABSTRACT: In this paper, we study the second-order nonlinear differential systems of Liénard-type
x
˙
=
1
a(
x
)
[
h(
y
)−F(
x
) ]
,
y
˙
=−a(
x
)g(
x
)
. Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.