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Normalized Solutions to at Least Mass Critical Problems: Singular Polyharmonic Equations and Related Curl–Curl Problems
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Normalized Solutions to at Least Mass Critical Problems: Singular Polyharmonic Equations and Related Curl–Curl Problems
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Journal Article
Normalized Solutions to at Least Mass Critical Problems: Singular Polyharmonic Equations and Related Curl–Curl Problems
2024
Overview
We are interested in the existence of normalized solutions to the problem
(
-
Δ
)
m
u
+
μ
|
y
|
2
m
u
+
λ
u
=
g
(
u
)
,
x
=
(
y
,
z
)
∈
R
K
×
R
N
-
K
,
∫
R
N
|
u
|
2
d
x
=
ρ
>
0
,
in the so-called at least mass critical regime. We utilize recently introduced variational techniques involving the minimization on the
L
2
-ball. Moreover, we find also a solution to the related curl–curl problem
∇
×
∇
×
U
+
λ
U
=
f
(
U
)
,
x
∈
R
N
,
∫
R
N
|
U
|
2
d
x
=
ρ
,
which arises from the system of Maxwell equations and is of great importance in nonlinear optics.
Publisher
Springer US,Springer Nature B.V
