3 problems

Let $d>1$, let $u_{\text{\tiny\rm gs}}$ be the ground state of the Gross–Pitaevskii eigenvalue problem (GPEVP), and let $V_\varepsilon$ be a disorder potential satisfying assumptio…

Let $d>1$, and let $u_{\text{\tiny\rm gs}}$ denote the ground state of the Gross–Pitaevskii eigenvalue problem (GPEVP). Higher-dimensional ground-state bound. The ground state sati…

Let $\widehat{\tau}$, $\widehat{g}$, and $\tau$ denote the parameters introduced in the model, and let $\epsilon$ tend to zero. Asymptotic interaction-parameter conjecture. … This…