In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system $-\Delta u+u^3+\beta u{v}^2=\lambda u,-\Delta v+v^3+\beta u^{2}v=\mu v,u,v\in H_0^1\left(\Omega \right),u,v>0$, as the interspecies scattering length $\beta$ goes to $+\infty$. For this system we consider the associated energy functionals $J_{\beta },\beta \in (0,+\infty )$, with $L^2$-mass constraints, which limit $J_{\infty }$ (as $\beta \to +\infty$) is strongly irregular. For such functionals, we construct multiple critical points via a common...

We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a segregated limiting profile, with the difference of its components satisfying a limit scalar PDE. In the case of radial symmetry, under natural non-degeneracy assumptions on a solution of the limit problem, we establish by a perturbation argument its persistence...