Affiliation:
1. Meishan High School
2. Civil Aviation Flight University of China
3. China West Normal University
Abstract
In this paper, we consider of the following second-order Hamiltonian system
u
¨
(
t
)
−
L
(
t
)
u
(
t
)
+
∇
W
(
t
,
u
(
t
)
)
=
0
,
∀
t
∈
R
,
where
W
(
t
,
x
)
is subquadratic at infinity. With a competition condition, we establish the existence of homoclinic solutions by using the variational methods. In our theorem, the smallest eigenvalue function
l
(
t
)
of
L
(
t
)
is not necessarily coercive or bounded from above and
W
(
t
,
x
)
is not necessarily integrable on
R
with respect to
t
. Our theorem generalizes many known results in the references.
Funder
Fundamental Research Funds for Central Universities