Full paper in PDF:
$%O. Lopes, Instability of radial standing waves of Schrödinger equation on the
exterior of a ball,
Rev. Mat. Complut. 12 (1999), no. 2, 537–545.%$
ABSTRACT
Under smoothness and growth assumptions on
we show that a standing
wave
of the Schrödinger equation on the exterior
of a
ball and Neumann boundary condition
where
is real and
is real and radially symmetric, is always linearly
unstable under perturbations in the space
. (It may be stable under
perturbations in
.)
The instability is independent of
having a fixed sign and of its Morse index.
The main tool is a theorem of linearized instability of M. Grillakis.
1991 Mathematics Subject Classification: 35Q55.