On the orbital stability of inhomogeneous nonlinear Schr\"{o}dinger equations with singular potential
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1601-1615
Published online August 6, 2019
Printed November 30, 2019
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.
Downloads: Full-text PDF   Full-text HTML


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd