I will present some existence results for a class of Choquard equations in which the potential has a positive limit at infinity and satisfies suitable decay assumptions. Also, it is taken invariant under the action of a closed subgroup of linear isometries of $\mathbb{R}^N$. As a consequence, the positive solution found is invariant under the same action. We investigate superlinear, linear and sublinear nonlinearities, and we take into account an arbitrary number of bumps.

Joint work together with Liliane Maia and Benedetta Pellacci.