  We study two non-local variational problems that are characterized by the
presence of a Riesz-like repulsive term that competes with an attractive term.
The first functional is defined on the subsets of $\mathbb{R}^N$ and has the
fractional perimeter $\mathcal{P}_s$ as attractive term. The second functional
instead is defined on $L^1(\mathbb{R}^N;[0,1])$ and contains an attractive term
of positive-power-type. For both of the functionals we prove that balls are the
unique minimizers in the appropriate volume constraint range, generalizing the
results already present in the literature for more specific energies.
