Symmetry breaking and multiple solutions for the Schrödinger–Poisson–Slater equation.

We study the Schrödinger–Poisson–Slater equation where p ∈ (2 , 3) , λ > 0 , V (x) ∈ C (R 3 , R +) and I 2 (x) : = (4 π | x |) - 1 is the Newtonian potential. We prove the nonexistence of nontrivial solutions, existence of positive nonradial (and radial) ground-state solutions, and mountain-pass-type solutions to (SPS), depending on the values of parameters p and λ . To our knowledge, this is the first study of the existence of ground-state solutions at positive energy levels when p ∈ (2 , 3) . Furthermore, we show that a symmetry breaking occurs for the ground-state solutions, which is a purely nonlocal phenomenon that cannot be observed in the local prototype case. [ABSTRACT FROM AUTHOR]