TITLE:
Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function
AUTHORS:
Jingxing Huang, Junhui Xie
KEYWORDS:
Logarithmic Schrödinger Equations, Weight Function, Constrained Minimization Method, Symmetric Mountain Pass Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.7,
July
30,
2024
ABSTRACT: This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem:
−div(
a(
x
)∇u
)+V(
x
)u=ulog
u
2
+k(
x
)
| u |
q
1
−2
u+h(
x
)
| u |
q
2
−2
u, x∈
ℝ
N
.
(1)We first prove that the corresponding functional I belongs to
C
1
(
H
V
1
(
ℝ
N
),ℝ
)
. Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).