Positive solutions for a class of singular quasilinear Schrodinger equations with critical Sobolev exponent

We prove the existence of positive solutions of the following singular quasilinear Schrodinger equations at critical growth -Delta u - lambda c(x)u - kappa alpha(Delta(vertical bar u vertical bar(2 alpha)))vertical bar u vertical bar(2 alpha-2) u = vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(2)*(-2)u, u is an element of D-1,D-2 (R-N), via variational methods, where lambda >= 0, c : R-N -> R+, kappa > 0, 0 < alpha < 1/2, 2 < q < 2*. It is interesting that we do not need to add a weight function to control vertical bar u vertical bar(q-2)u. (C) 2018 Elsevier Inc. All rights reserved.