We consider the Cauchy problem for nonlinear Schrödinger equations in the presence of a smooth, possibly unbounded, potential. No assumption is made on the sign of the potential. If the potential grows at most linearly at infinity, we construct solutions in Sobolev spaces (without weight), locally in time. Under some natural assumptions, we prove that the H… (More)

@inproceedings{Carles2007OnTC,
title={On the Cauchy problem in Sobolev spaces for nonlinear Schrodinger equations with potential},
author={R{\'e}mi Carles},
year={2007}
}