Affiliation:
1. University of Shanghai for Science and Technology
Abstract
This paper establishes the multiplicity of solutions for a class of quasilinear Schrödinger elliptic equations:
−
Δ
u
+
V
(
x
)
u
−
γ
2
Δ
(
u
2
)
u
=
f
(
x
,
u
)
,
x
∈
R
3
,
where
V
(
x
)
:
R
3
→
R
is a given potential and
γ
>
0
. Furthermore, by the variational argument and
L
∞
-estimates, we are able to obtain the precise asymptotic behavior of these solutions as
γ
→
0
+
.