2 problems

Let $U_0$ be the nonlinear interaction coefficient, let $\mu$ be the chemical potential, and let $(\mathcal{E}_n,\phi_n)$ be an eigenvalue and eigenfunction of the associated linea…

Let $m>0$, and let $\mathcal{S}_m$ denote the set of stationary solutions with total mass $m$. Let $Q_{gs}$ be a ground state, and let $E[Q]$ denote the total energy of a stationar…