Multiplicity And Concentration Results For A Class Of Singularly Perturbed Critical Quasilinear Schrodinger Equation

In this paper, we study a class of singularly perturbed critical quasilinear Schrodinger equation of the form-epsilon(2) Delta u + V(x)u - epsilon(2) (Delta u(2))u = P(x)vertical bar u vertical bar(p-2)u + Q(x)vertical bar u vertical bar(2-2)* (2)u, in R-N.By using a change of variables and variational argument, we prove not only the existence of positive ground state solutions and their concentration behavior, but also the existence and associated concentration behavior of multiple solutions.