Ground States to the Generalized Nonlinear Schrödinger Equations with Bernstein Symbols

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

Jinmyoung Seok

Younghun Hong

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    Jin, Sangdon

    Discrete and Continuous Dynamical Systems, Vol. 42 (2022), Iss. 7 P.3103

    https://doi.org/10.3934/dcds.2022010 [Citations: 0]