In this paper, we consider the following zero mass Schrödinger–Bopp–Podolsky system: \( {\left\{ \begin{array}{ll} -\varDelta u +q^2\phi u=|u|^{p-2}u,\\ -\varDelta \phi +a^2\varDelta ^2\phi =4\pi u^2, \end{array}\right. } {\text { in }} \mathbb {R}^N, \) where \(a>0\) and \(q\ne 0\) . We complete the study initiated in [2], which relied on a perturbation argument to establish the existence of weak solutions. Here, in contrast, our approach, based on the Mountain Pass Theorem and the splitting lemma, directly yields a ground state solution for \(p \in (4,6)\) . Moreover, by deriving a Pohozaev identity, we further obtain some nonexistence results for suitable p. Finally, based on the minimax characterization, we also analyze, in the radial case, the asymptotic behavior of the solutions obtained as \(a\rightarrow 0\) , thereby establishing a link with the zero mass Schrödinger–Poisson system.
