数学物理学报(英文版) ›› 1996, Vol. 16 ›› Issue (4): 421-431.
李用声, 陈庆益
Li Yongsheng, Chen Qingyi
摘要: In this paper we consider tile initial boundary value problems for the nonlinear Schrödinger equation
iut+△u+f(|u|2)u=0, t ≥ 0, x∈Ω, u(0,x)=u0(x), x∈Ω
with boundary conditions u(t,x)|∂Ω=0 or ∂u/∂v|∂Ω=0 where Ω=Rn\B(0,1) is the exterior domain of the unit ball B(0,1).We prove that the smooth,radially symmetric solutions of the problem exists globally and uniquely when|f(s)|≤ Cs(p-1)/2 and 1 ≤ p< 5 and also prove that the solutions blow up when f(s)=λs(p-1)/2(λ>0) and p ≥ 5 under appropriate conditions on no and obtain some properties for blow-up solutions.