Clara E. Garza-Hume, Pablo Padilla
Abstract:
We consider a semi-linear elliptic equation on the sphere
with
odd and
subcritical nonlinearity. We show that given any positive
integer
,
if the exponent
of the nonlinear term
is sufficiently close to the critical Sobolev exponent
,
then there exists a positive solution with
peaks. Moreover,
the minimum energy solutions with
peaks are such that the centers
of these concentrations converge as
to the solution of
an underlying geometrical problem, namely,
arranging
points on
so they are as far away
from each other as possible.
Published February 28, 2007.
Math Subject Classifications: 35B33, 35J20.
Key Words: Semilinear elliptic equation; sphere packing;
critical Sobolev exponent; pattern formation.
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Clara E. Garza-Hume IIMAS-FENOMEC, Universidad Nacional Autónoma de México Circuito Escolar, Cd. Universitaria 04510 México D. F., México email: clara@mym.iimas.unam.mx | |
Pablo Padilla IIMAS-FENOMEC, Universidad Nacional Autónoma de México Circuito Escolar, Cd. Universitaria 04510 México D. F., México email: pablo@mym.iimas.unam.mx |
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