@Article{JMS-50-3,
author = {Ze, Li and Zhao, Lifeng},
title = {Decay and Scattering of Solutions to Nonlinear Schrödinger Equations with Regular Potentials for Nonlinearities of Sharp Growth},
journal = {Journal of Mathematical Study},
year = {2017},
volume = {50},
number = {3},
pages = {277--290},
abstract = {<p style="text-align: justify;">In this paper, we prove the decay and scattering in the energy space for nonlinear
Schrödinger equations with regular potentials in $\mathbb{R}^d$ namely, $i∂_tu+Δu-V(x)u+
λ|u|^{p-1}u=0$. We will prove decay estimate and scattering of the solution in the small
data case when $1+\frac{2}{d}&lt;p ≤ 1+\frac{4}{d-2}, d ≥ 3$. The index $1+\frac{2}{d}$&nbsp; is sharp for scattering concerning the result of Strauss [22]. This result generalizes the one-dimensional work of
Cuccagna et al. [4] to all $d ≥ 3$.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v50n3.17.05},
url = {https://global-sci.com/article/87775/decay-and-scattering-of-solutions-to-nonlinear-schrodinger-equations-with-regular-potentials-for-nonlinearities-of-sharp-growth}
}