Positive solutions for a critical quasilinear Schrödinger equation

In our current work we investigate the following critical quasilinear Schrödinger equation

$$-\mathrm{\Delta }\mathrm{\Theta }+\mathcal{V}(x)\mathrm{\Theta }-\mathrm{\Delta }({\mathrm{\Theta }}^2)\mathrm{\Theta }=|\mathrm{\Theta }{|}^{{22}^{\ast }-2}\mathrm{\Theta }+\lambda \mathcal{K}(x)g(\mathrm{\Theta }),x\in {\mathbb{R}}^N,$$

where $N\ge 3$, $\lambda >0$, $\mathcal{V},\mathcal{K}\in C({\mathbb{R}}^N,{\mathbb{R}}^{+})$ and $g\in C(\mathbb{R},\mathbb{R})$ has a quasicritical growth condition. We use the dual approach and the mountain pass theorem to show that the considered problem has a positive solution when $\lambda$ is a large parameter.