Ground and bound states for a static Schrödinger-Poisson-Slater problem

We study a static version of the Schroedinger–Poisson–Slater equation, with a power nonlinear term. The case when the power p < 2 being already studied, we consider here p ≥ 2. For p > 2 we study both the existence of ground and bound states. It turns out that p = 2 is critical in a certain sense, and will be studied separately. Finally, we prove that radial solutions satisfy a point-wise exponential decay at infinity for p > 2