Abstract
In this paper, we study the following Schrödinger system with coercive potential
{
−
Δ
u
+
V
1
(
x
)
u
=
λ
1
u
+
F
u
(
u
,
v
)
in
ℝ
N
,
−
Δ
v
+
V
2
(
x
)
v
=
λ
2
v
+
F
v
(
u
,
v
)
in
ℝ
N
,
∫
ℝ
N
|
u
|
2
d
x
=
a
and
∫
ℝ
N
|
v
|
2
d
x
=
b
,
where
a
,
b
>
0
,
N
≥
3
,
λ
1
,
λ
2
∈
ℝ
are Lagrange mulitipliers. For sufficiently small mass parameters
a
,
b
>
0
, we establish that the system possesses two distinct solutions: a local minimizer and a mountain pass type solution. Furthermore, we prove that the local minimizer is a ground state solution under certain monotonicity conditions.