A $p$-Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities

Let $Ω\subset\R^N$, $N\ge2$, be a bounded domain and let $1<p<\infty$. Inspired by the exponential case treated in \cite{BO2026}, we study the quasilinear Schrödinger--Maxwell system \[ \begin{cases} -Δ_p u+ψG'(u)=f &\text{in }Ω,\\ -Δ_pψ=G(u) &\text{in }Ω,\\ u=ψ=0 &\text{on }\partialΩ, \end{cases} \