The fibering method approach for a non-linear schrödinger equation coupled with the electromagnetic field

We study, with respect to the parameter q 6 ≠ 0, the following Schrödinger- Bopp-Podolsky system in R3{equation presented} where p ϵ (2; 3], ω > 0, a ≥ 0 are fixed. We prove, by means of the fibering approach, that the system has no solutions at all for large values of q and has two radial solutions for small q's. We give also qualitative properties about the energy level of the solutions and a variational characterization of these extremal values of q. Our results recover and improve some results in [2, 5].