The mass-mixed case for normalized solutions to NLS equations in
dimension two
The mass-mixed case for normalized solutions to NLS equations in
dimension two
\noindent We are concerned with positive normalized solutions $(u,\lambda)\in H^1(\mathbb{R}^2)\times\mathbb{R}$ to the following semi-linear Schr\"{o}dinger equations $$ -\Delta u+\lambda u=f(u), \quad\text{in}~\mathbb{R}^2, $$ satisfying the mass constraint $$\int_{\mathbb{R}^2}|u|^2\, dx=c^2\ .$$ We are interested in the so-called mass mixed case in which $f$ has $L^2$-subcritical growth at zero and critical growth at …