@article{Meng2022, 
author = {Yali Meng},
title = {Existence of stable standing waves for the nonlinear Schrödinger equation with attractive inverse-power potentials},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {5957-5970},
keywords = {nonlinear Schrödinger equation, inverse-power potentials, stable standing waves},
url = {https://www.sciopen.com/article/10.3934/math.2022332},
doi = {10.3934/math.2022332},
abstract = {In this paper, we consider the following nonlinear Schrödinger equation with attractive inverse-power potentials     i      ∂    t    ψ  +  Δ  ψ  +  γ      |    x            |              −      σ        ψ  +      |    ψ            |        α    ψ  =  0  ,        (  t  ,  x  )  ∈      R    ×            R        N    ,where    N  ≥  3,    0  <  γ  <  ∞,    0  <  σ  <  2 and        4    N    <  α  <      4          N      −      2      . By using the concentration compactness principle and considering a local minimization problem, we prove that there exists a        γ    0    >  0 sufficiently small such that    0  <  γ  <      γ    0   and for any    a  ∈  (  0  ,      a    0    ), there exist stable standing waves for the problem in the        L    2  -supercritical case. Our results are complement to the result of Li-Zhao in [23].}
}