Abstract
In this paper, we study the following generalized quasilinear
Schrödinger equation
−
div
(
g
2
(
u
)
∇
u
)
+
g
(
u
)
g
′
(
u
)
|
∇
u
|
2
+
V
(
x
)
u
=
λ
f
(
x
,
u
)
+
h
(
x
,
u
)
,
x
∈
R
N
,
where
λ
>
0
,
N
≥
3
,
g
∈
C
1
(
R
,
R
+
)
. By using a change of
variable, we obtain the existence of positive solutions for this problem
with concave and convex nonlinearities via the Mountain Pass Theorem. Our
results generalize some existing results.
Cited by
2 articles.
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