Singular quasilinear critical Schrödinger equations in $ \mathbb {R}^N $

We prove multiplicity results for solutions, both with positive and negative energy, for a class of singular quasilinear Schrödinger equations in the entire \begin{document}$ \mathbb {R}^N $\end{document} involving a critical term, nontrivial weights and positive parameters \begin{document}$ \lambda $\end{document}, \begin{document}$ \beta $\end{document}, covering several physical models, coming from plasma physics as well as high-power ultra short laser in matter. Also the symmetric setting is investigated. Our proofs relay on variational tools, including concentration compactness principles because of the delicate situation of the double lack of compactness. In addition, a necessary reformulation of the original problem in a suitable variational setting, produces a singular function, delicate to be managed.