= Classification of Weinstein-functional minimizers
Every minimizer of the <Weinstein functional> has the form
$$
u(x)=aQ(b(x-x_0)),
\qquad
a\in\mathbb C\setminus\{0\},\quad b>0,\quad x_0\in\mathbb R^d,
$$
where $Q$ is the positive radial <NLS ground state>. The <Euler-Lagrange equation> first reduces a minimizer to a rescaled ground-state equation; the equality cases in the diamagnetic and rearrangement inequalities give the constant phase, translation, and radial profile.
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