| Abstract: | This paper concerns with existence and qualitative properties of ground states to generalized nonlinear Schr(o)dinger 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 H1-subcritical nonlinearity,even if the natural energy space does not control the H1-subcritical nonlinearity. |
