An Ohta–Kawasaki model set on the space

We examine a nonlocal diffuse interface energy with Coulomb repulsion in three dimensions inspired by the Thomas–Fermi–Dirac–von Weizsäcker, and the Ohta–Kawasaki models. We consider the corresponding mass-constrained variational problem and show the existence of minimizers for small masses, and the absence of minimizers for large masses.