X. Wang et Jc. Wei, Shift and stability of ground states of a nonlinear Schrodinger equation outside a small insulated domain, J DIFF EQUA, 154(1), 1999, pp. 73-95
We study the behavior and stability of ground states of a Neumann problem i
n the exterior of a shrinking domain. We show that the ground states concen
trate at a finite point which is a global maximum point of some function re
lated to the domain. Then we use this result to prove the stability of the
corresponding solitary waves of the time-dependent nonlinear Schrodinger eq
uation. (C) 1999 Academic Press.