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.
Yonggeun Cho, Misung Lee
Chonbuk National University; Chonbuk National University
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.
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