Existence and concentration result for a quasilinear Schrodinger equation with critical growth

This paper is concerned with the concentration of positive ground states solutions for a modified Schrodinger equation -epsilon(2)Delta u + V(x)u - epsilon(2)Delta(u(2))u = K(x)vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(22*-2)u, in R-N, where 4 < p < 22*, epsilon > 0 is a parameter and 2* := 2N/N-2 (N >= 3) is the critical Sobolev exponent. We prove the existence of a positive ground state solution v(epsilon) and epsilon sufficiently small under some suitable conditions on the nonnegative functions V(x) and K(x). Moreover, v(epsilon) concentrates around a global minimum point of V as epsilon -> 0. The proof of the main result is based on minimax theorems and concentration compact theory.