Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2019; 56(6): 1601-1615

Online first article August 6, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b190029

Copyright © The Korean Mathematical Society.

On the orbital stability of inhomogeneous nonlinear Schr\"{o}dinger equations with singular potential

Yonggeun Cho, Misung Lee

Chonbuk National University; Chonbuk National University

Abstract

We show the existence of ground state and orbital stability of standing waves of nonlinear Schr\"{o}dinger equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in \cite{guz, din} slightly in 3 dimensions.

Keywords: inhomogeneous NLS, singular potential, ground state, orbital stability, well-posedness, Strichartz solution

MSC numbers: 35Q40, 35Q55

Supported by: This work was supported by NRF-2018R1D1A3B07047782.