Ground state and multiple solutions for Schrödinger-Bopp-Podolsky system with critical nonlinearity

In this paper, we study the following nonlinear Schrödinger-Bopp-Podolsky system: −∆u + u + l(x)φu = a(x)|u|p−2u + µb(x)|u|q−2u + |u|5, in R3, −∆φ + a2∆2φ = l(x)u2, in R3, where p,q ∈ (4,6), µ > 0, l(x), a(x) and b(x) are nonnegative continuous functions. Under some certain assumptions, we prove the above system have ground state and multiple solutions by using variational.