Multiplicity of solutions for Schrödinger–Bopp–Podolsky systems.

In this paper, we study the existence and multiplicity of solutions for the Schrödinger–Bopp–Podolsky system { - Δ ⁢ u + V ⁢ (x) ⁢ u + ϕ ⁢ u = f ⁢ (u) + λ ⁢ | u | 4 ⁢ u in ⁢ ℝ 3 , - Δ ⁢ ϕ + a 2 ⁢ Δ 2 ⁢ ϕ = 4 ⁢ π ⁢ u 2 in ⁢ ℝ 3 , where x ∈ ℝ 3 , a > 0 , V ⁢ (x) ∈ 풞 ⁢ (ℝ 3 , ℝ) . Using variational methods and the symmetric mountain pass theorem, we establish the existence of multiple solutions for this system. [ABSTRACT FROM AUTHOR]