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.