In this paper, we are concerned with the following Schrödinger-Poisson system with nonhomogeneous boundary conditions
{
−
1
2
△
u
+
ϕ
u
=
ω
u
,
a
m
p
;
in
Ω
,
−
△
ϕ
=
4
π
u
2
,
a
m
p
;
in
Ω
,
ϕ
=
h
,
u
=
0
,
a
m
p
;
on
∂
Ω
,
\begin{equation*} \begin {cases} -\frac {1}{2}\triangle {u}+\phi u =\omega u, & \text {in }\Omega , \\ -\triangle {\phi }=4\pi u^2, & \text {in } \Omega ,\\ \phi =h,u=0, & \text {on } \partial \Omega , \end{cases} \end{equation*}
where
Ω
\Omega
is a smooth and bounded domain in
R
3
\mathbb {R}^3
,
h
h
is a given nonnegative regular function on
∂
Ω
\partial \Omega
and
ω
∈
R
\omega \in \mathbb {R}
. By using variational method and bifurcation theory, we obtain the existence of positive solutions to the above system for
ω
\omega
larger than some positive constant.