Ground state solutions for the nonlinear Schrödinger-Bopp-Podolsky systems with nonperiodic potentials

In this article we study the existence of ground-state solutions for the Schro ̈dinger-Bopp-Podolsky equations −∆u+V(x)u+φu=f(x,u) inR3 −∆φ + a2∆2φ = 4πu2 in R3, where V ∈ C (R3 , R) has different forms on the half spaces, i.e. V (x) = V1 (x) for x1 > 0, and V (x) = V2(x) for x1 < 0, where V1,V2 ∈ C(R3) are periodic in each coordinate. The nonlinearity f is superlinear at infinity with subcritical or critical growth.