On an electromagnetic Schrödinger equation with critical growth
In this paper we consider the electromagnetic Schrödinger problem ( − i ∇ + A ) 2 u + λ V ( x ) u = K ( x ) | u | 2 ∗ − 2 u , in H A , V + 1 ( R N ) (see the definition in Section 1). According as whether the indefinite linear is resonant or nonresonant, we structure different direct sums of H A ,...
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| Veröffentlicht in: | Nonlinear analysis 2008-12, Vol.69 (11), p.4088-4098 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper we consider the electromagnetic Schrödinger problem
(
−
i
∇
+
A
)
2
u
+
λ
V
(
x
)
u
=
K
(
x
)
|
u
|
2
∗
−
2
u
, in
H
A
,
V
+
1
(
R
N
)
(see the definition in Section
1). According as whether the indefinite linear is resonant or nonresonant, we structure different direct sums of
H
A
,
V
+
1
(
R
N
)
. Then by applying the linking theorem twice to the corresponding functional we establish the existence results. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2007.10.039 |