An Existence Result for a Class of Magnetic Problems in Exterior Domains

• Published in: Milan journal of mathematics Vol. 89; no. 2; pp. 523 - 550
• Main Authors: Alves, Claudianor O., Ambrosio, Vincenzo, Ledesma, César E. Torres
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-12-2021
• Subjects: Analysis; Mathematics; Mathematics and Statistics; 35J10; Variational methods; 35A15; 35J61; Semilinear elliptic equations; Schrödinger equation
• ISSN: 1424-9286; 1424-9294
• DOI: 10.1007/s00032-021-00340-z

In this paper we deal with the existence of solutions for the following class of magnetic semilinear Schrödinger equation
(
P
)
(
-
i
∇
+
A
(
x
)
)
2
u
+
u
=
|
u
|
p
-
2
u
,
in
Ω
,
u
=
0
on
∂
Ω
,
where
N
≥
3
,
Ω
⊂
R
N
is an exterior domain,
p
∈
(
2
,
2
∗
)
with
2
∗
=
2
N
N
-
2
, and
A
:
R
N
→
R
N
is a continuous vector potential verifying
A
(
x
)
→
0
as
|
x
|
→
∞
.