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 - <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>