CRITICAL SINGULAR PROBLEMS ON UNBOUNDED DOMAINS
We present some results of existence for the following problem: − Δ u = a ( x ) g ( u ) + u | u | 2∗−2 , x ∈ ℝ N ( N ≥ 3), u ∈ D 1,2 ( ℝ N ), where the function a is a sign‐changing function with a singularity at the origin and g has growth up to the Sobolev critical exponent 2 ∗ = 2 N /( N − 2)....
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| Veröffentlicht in: | Abstract and Applied Analysis 2005-01, Vol.2005 (6), p.639-653 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We present some results of existence for the following problem: −
Δ
u
=
a
(
x
)
g
(
u
) +
u
|
u
|
2∗−2
,
x
∈
ℝ
N
(
N
≥ 3),
u
∈
D
1,2
(
ℝ
N
), where the function
a
is a sign‐changing function with a singularity at the origin and
g
has growth up to the Sobolev critical exponent 2
∗
= 2
N
/(
N
− 2). |
|---|---|
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/AAA.2005.639 |