3 problems

Let $N\geq 1$, $\gamma>0$, $\mu>0$, $c>0$, and $2+\frac{4}{N}<q<2^*$. Let $\omega_1$ and $\omega_2$ be the parameters appearing in the condition governing the existence of normaliz…

For $b\in(0,1)$ and sufficiently large mass $c1$, the Gross–Pitaevskii–Poisson problem has mountain pass solutions of type I and type II, constructed respectively by Theorems 1 and…

Let $u_bb$ be a fixed-frequency ground state of the Gross–Pitaevskii–Poisson equation with small frequency parameter $bb>0$, and let $\rho_bb:=|u_bb|_2>0$ be its mass. Mountain pas…