Homoclinic solutions for a class of second-order Hamiltonian systems

• Published in: Nonlinear analysis Vol. 71; no. 3; pp. 1140 - 1152
• Main Authors: Tang, X.H., Xiao, Li
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01-08-2009; Elsevier
• Subjects: Diagonal method; Exact sciences and technology; Global analysis, analysis on manifolds; Hamiltonian systems; Homoclinic solutions; Mathematical analysis; Mathematics; Mountain Pass theorem; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Mountain Pass theorem; 34C37; Hamiltonian systems; 58E05; Homoclinic solutions; 70H05; Diagonal method; Second order equation; Nonlinear analysis; Hamiltonian system; Mathematical model; Hamiltonian
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2008.11.038

Some new results for the existence of homoclinic orbits are obtained for the second-order Hamiltonian systems
u
̈
(
t
)
+
∇
V
(
t
,
u
(
t
)
)
=
f
(
t
)
, where
t
∈
R
,
u
∈
R
n
and
V
∈
C
1
(
R
×
R
n
,
R
)
,
V
(
t
,
x
)
=
−
K
(
t
,
x
)
+
W
(
t
,
x
)
is
T
-periodic with respect to
t
,
T
>
0
and
f
:
R
→
R
n
is a continuous and bounded function. Our assumptions on
K
and
f
are rather loose.