Loading…
Ground state and nodal solutions for critical Schrödinger–Kirchhoff-type Laplacian problems
In this paper, we are interested in the existence of ground state nodal solutions for the following Schrödinger–Kirchhoff-type Laplacian problems: - M ( ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = | u | 4 u + k f ( u ) , x ∈ R 3 , where M ( t ) = a + b t γ with 0 < γ < 2 , a , b > 0 and the non...
Saved in:
| Published in: | Journal of fixed point theory and applications 2021-08, Vol.23 (3), Article 34 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we are interested in the existence of ground state nodal solutions for the following Schrödinger–Kirchhoff-type Laplacian problems:
-
M
(
∫
R
3
|
∇
u
|
2
d
x
)
Δ
u
+
V
(
x
)
u
=
|
u
|
4
u
+
k
f
(
u
)
,
x
∈
R
3
,
where
M
(
t
)
=
a
+
b
t
γ
with
0
<
γ
<
2
,
a
,
b
>
0
and the nonlinear function
f
∈
C
(
R
,
R
)
. By the nodal Nehari manifold method, for each
b
>
0
, we obtain a least energy nodal solution
u
b
and a ground state solution
v
b
of this problems when
k
≫
1
. Our results improve and extend the known results of the usual case
γ
=
1
in the sense that a more wider range of
γ
is covered. |
|---|---|
| ISSN: | 1661-7738 1661-7746 |
| DOI: | 10.1007/s11784-021-00870-4 |