Concentration of Positive Solutions for Critical Quasilinear Schrödinger Equation with Competing Potentials

In this paper, we study a class of singularly perturbed critical quasilinear Schrodinger equation of the form - e2 u + V( x) u - e2( u2) u = P( x)| u| p- 2u + Q( x)| u| 2 center dot 2 *- 2u, inRN. By using a change of variables and variational argument, we prove the existence of positive solutions and their concentration behavior.