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research
Asymptotic behaviour of a semilinear elliptic system with a large exponent
Authors
Adimurthi
B. Gidas
+17Â more
C.-S. Lin
D. Gilbarg
D.G. Figueiredo De
D.R. Adams
E. Mitidieri
F. Takahashi
G. Talenti
G. Talenti
H. Brezis
I. A. Guerra
J. Wei
M. Flucher
P. Quittner
Ph. Clement
R.C.A.M Vorst van der
X. Ren
X. Ren
Publication date
1 January 2006
Publisher
'Springer Science and Business Media LLC'
Doi
Cite
View
on
arXiv
Abstract
Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad \Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where
Ω
\Omega
Ω
is a bounded convex domain in
R
N
,
\R^N,
R
N
,
N
>
2
,
N>2,
N
>
2
,
with smooth boundary
∂
Ω
.
\partial \Omega.
∂
Ω.
We study the asymptotic behaviour of the least energy solutions of this system as
p
→
∞
.
p\to \infty.
p
→
∞.
We show that the solution remain bounded for
p
p
p
large and have one or two peaks away form the boundary. When one peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio
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Last time updated on 01/04/2019