Type: Article

Small solutions to the nonlinear Schrödinger equation with a nonlinear Neumann boundary condition

Nakao Hayashi, Elena I Kaikina, Takayoshi Ogawa;

Abstract:

We consider the nonlinear Schrödinger equations with a power nonlinearity of order 2 q? 1 and a nonlinear Neumann boundary conditions with a power nonlinearity of order q. Our purpose in this paper is to prove that if q is in an interval between L 1 critical case q= 2 and L 2 critical one q= 3, namely 2< q< 3 and the data are small, then there exists a unique global solutions.