Year: 2021
Author: Jinmyoung Seok, Younghun Hong
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 2 : pp. 157–177
Abstract
This paper concerns with existence and qualitative properties of ground states to generalized nonlinear Schrödinger equations (gNLS) with abstract symbols. Under some structural assumptions on the symbol, we prove a ground state exists and it satisfies several fundamental properties that the ground state to the standard NLS enjoys. Furthermore, by imposing additional assumptions, we construct, in small mass case, a nontrivial radially symmetric solution to gNLS with $H^1$-subcritical nonlinearity, even if the natural energy space does not control the $H^1$-subcritical nonlinearity.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2021.pr80.06
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 2 : pp. 157–177
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Generalized NLS solitary waves variational methods Bernstein symbols.
Author Details
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Orbital stability for the mass-critical and supercritical pseudo-relativistic nonlinear Schrödinger equation
Hong, Younghun
Jin, Sangdon
Discrete and Continuous Dynamical Systems, Vol. 42 (2022), Iss. 7 P.3103
https://doi.org/10.3934/dcds.2022010 [Citations: 0]