@Article{ATA-37-157,
author = {Seok , Jinmyoung and Hong , Younghun},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2021.pr80.06},
url = {http://global-sci.org/intro/article_detail/ata/18769.html}
}