Nonlinear Schrödinger Equation with Inhomogeneous Dirichlet Boundary Data

@inproceedings{Bu2005NonlinearSE,
  title={Nonlinear Schr{\"o}dinger Equation with Inhomogeneous Dirichlet Boundary Data},
  author={Charles Bu and Kimitoshi Tsutaya and Chenying Zhang},
  year={2005}
}
In this article we study the following nonlinear Schrodinger equation iut=Δu−g∣u∣p−1u in a domain Ω⊂Rn with initial condition u(x,0)=ϕ(x) and the Dirichlet boundary condition u(x,t)=Q(x,t) on ∂Ω, where ϕ, Q are given smooth functions. The nonlinear term contributes a negative term to the energy (i.e., g<0). We present the existence theorem for a global solution of finite energy when p⩽1+2∕n.