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This paper concerns the existence of positive ground state solutions forgeneralized quasilinear Schr\"odinger equations in $\mathbb{R}^N$ with criticalgrowth which arise from plasma physics, as well as high-power ultrashort laserin matter. By applying a variable replacement, the quasilinear problem reducesto a semilinear problem which the associated functional is well defined in theSobolev space $H^1(\mathbb{R}^N)$. We use the method of Nehari manifold for themodified equation, establish the minimax characterization, then obtain eachPalais-Smale sequence of the associated energy functional is bounded. Bycombining Lions's concentration-compactness lemma together with some classicalarguments developed by Br\'ezis and Nirenberg \cite{bn}, we establish that thebounded Palais-Smale sequence has a nonvanishing behaviour. Finally, we obtainthe existence of a positive ground state solution under some appropriateassumptions. Our results extend and generalize some known results.

Positive ground state solutions for generalized quasilinear Schr\"odinger equations with critical growth