On the elliptic problems involving multi-singular inverse square potentials and critical Sobolev exponent
Assume that Ω ⊂ R N ( N ≥ 3 ) is a smooth bounded domain, a i are different points in Ω , i = 1 , 2 , … , k , k ≥ 2 , λ > 0 , 2 ≤ q < 2 ∗ , μ < μ ̄ ≔ ( N − 2 2 ) 2 , 2 ∗ = 2 N N − 2 is the critical Sobolev exponent. We study the existence and asymptotic behavior of solutions to the multi-si...
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Veröffentlicht in: | Nonlinear analysis 2008-05, Vol.68 (10), p.3050-3066 |
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1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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Zusammenfassung: | Assume that
Ω
⊂
R
N
(
N
≥
3
)
is a smooth bounded domain,
a
i
are different points in
Ω
,
i
=
1
,
2
,
…
,
k
,
k
≥
2
,
λ
>
0
,
2
≤
q
<
2
∗
,
μ
<
μ
̄
≔
(
N
−
2
2
)
2
,
2
∗
=
2
N
N
−
2
is the critical Sobolev exponent. We study the existence and asymptotic behavior of solutions to the multi-singular critical elliptic problem
−
Δ
u
−
μ
u
∏
i
=
1
k
|
x
−
a
i
|
2
=
|
u
|
2
∗
−
2
u
+
λ
|
u
|
q
−
2
u
with Dirichlet boundary condition. The results depend crucially on the parameters
λ
,
μ
and
q
. |
---|---|
ISSN: | 0362-546X 1873-5215 |
DOI: | 10.1016/j.na.2007.01.073 |