Affiliation:
1. College of Science, Hunan University of Technology and Business , 410205 Changsha , Hunan , China
Abstract
Abstract
This article is concerned with the following Hamiltonian elliptic system:
−
ε
2
Δ
u
+
ε
b
→
⋅
∇
u
+
u
+
V
(
x
)
v
=
H
v
(
u
,
v
)
in
R
N
,
−
ε
2
Δ
v
−
ε
b
→
⋅
∇
v
+
v
+
V
(
x
)
u
=
H
u
(
u
,
v
)
in
R
N
,
\left\{\begin{array}{l}-{\varepsilon }^{2}\Delta u+\varepsilon \overrightarrow{b}\cdot \nabla u+u+V\left(x)v={H}_{v}\left(u,v)\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\\ -{\varepsilon }^{2}\Delta v-\varepsilon \overrightarrow{b}\cdot \nabla v+v+V\left(x)u={H}_{u}\left(u,v)\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\end{array}\right.
where
ε
>
0
\varepsilon \gt 0
is a small parameter,
V
V
is a potential function, and
H
H
is a super-quadratic sub-critical Hamiltonian. Applying suitable variational arguments and refined analysis techniques, we construct a new multiplicity result of semiclassical solutions which depends on the number of global minimum points of
V
V
. This result indicates how the shape of the graph of
V
V
affects the number of semiclassical solutions.
Cited by
20 articles.
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