Ground states of a prescribed mean curvature equation
Ignacio Guerra
Universidad de Santiago de Chile
email: iguerra@usach.cl
Abstract:
We study the existence of radial ground-state solutions for the
problem
, . It is known that this problem has infinitely
many ground states when
, while no solutions exist if
. A question raised by Ni and Serrin in [Atti Convegni
Lincei 77 (1985), 231-257], is whether or not ground state solutions
exist for
In this paper we prove the
existence of a large, finite number of ground states with fast decay
as
provided that lies below but close
enough to the critical exponent
. These solutions develop a
bubble towerprofile as approaches the critical exponent.
This is joint work with Manuel del Pino (Universidad de Chile)