Anal. Theory Appl., 37 (2021), pp. 157-177.
Published online: 2021-04
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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} }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.