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In this paper, we study a class of quasilinear Schr\"{o}dinger equation ofthe form $$-\varepsilon^2\Deltau+V(x)u-\varepsilon^2(\Delta(|u|^{2\alpha}))|u|^{2\alpha-2}u&=&\lambda|u|^{q-2}u+|u|^{2^*(2\alpha)-2}u,\quad\mbox{in}{\mathbb{R}}^N, $$where $\varepsilon>0,\lambda>0,q\geq2,\alpha>1/2$ are constants, $N\geq3$. Byusing change of variable and variational approach, the existence of positivesolution which has a local maximum point and decays exponentially is obtained.

Solutions for a class of quasilinear Schr\"{o}dinger equations with critical exponents term