TY - JOUR
T1 - Decay and Scattering of Solutions to Nonlinear Schrödinger Equations with Regular Potentials for Nonlinearities of Sharp Growth
AU - Li , Ze
AU - Zhao , Lifeng
JO - Journal of Mathematical Study
VL - 3
SP - 277
EP - 290
PY - 2017
DA - 2017/09
SN - 50
DO - http://doi.org/10.4208/jms.v50n3.17.05
UR - https://global-sci.org/intro/article_detail/jms/10621.html
KW - Nonlinear Schrödinger equations, potential, decay, scattering.
AB - <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>