Abstract
UDC 517.9
We investigate a class of Hamiltonian systems
-
q
'
'
(
t
)
+
(
L
(
t
)
-
ξ
)
q
(
t
)
=
a
(
t
)
|
q
(
t
)
|
p
-
2
q
(
t
)
+
η
f
(
t
)
,
q
∈
H
1
(
ℝ
,
ℝ
N
)
,
where
(
t
,
q
)
∈
ℝ
×
ℝ
N
,
p
>
2
,
a
∈
C
(
ℝ
,
(
0
,
+
∞
)
)
,
f
∈
C
(
ℝ
,
ℝ
N
)
,
ξ
,
η
are real parameters, and
L
∈
C
(
ℝ
,
ℝ
N
2
)
is a positive definite symmetric matrix for all
t
∈
ℝ
.
The main technical approach is based on the Nehari manifold method combined with variational and topological methods. The obtained results extend and complement the results available in the literature.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)