Volume 37, Issue 2
Ground States to the Generalized Nonlinear Schrödinger Equations with Bernstein Symbols

Jinmyoung Seok & Younghun Hong

Anal. Theory Appl., 37 (2021), pp. 157-177.

Published online: 2021-04

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  • 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.

  • Keywords

Generalized NLS, solitary waves, variational methods, Bernstein symbols.

  • AMS Subject Headings

35J35, 35J61

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-37-157, author = {Jinmyoung and Seok and and 14888 and and Jinmyoung Seok and Younghun and Hong and and 14889 and and Younghun Hong}, title = {Ground States to the Generalized Nonlinear Schrödinger Equations with Bernstein Symbols}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {37}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.pr80.06}, url = {http://global-sci.org/intro/article_detail/ata/18769.html} }
TY - JOUR T1 - Ground States to the Generalized Nonlinear Schrödinger Equations with Bernstein Symbols AU - Seok , Jinmyoung AU - Hong , Younghun JO - Analysis in Theory and Applications VL - 2 SP - 157 EP - 177 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/ata.2021.pr80.06 UR - https://global-sci.org/intro/article_detail/ata/18769.html KW - Generalized NLS, solitary waves, variational methods, Bernstein symbols. AB -

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.

Jinmyoung Seok & Younghun Hong. (1970). Ground States to the Generalized Nonlinear Schrödinger Equations with Bernstein Symbols. Analysis in Theory and Applications. 37 (2). 157-177. doi:10.4208/ata.2021.pr80.06
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