Quasilinear Schrodinger equations with unbounded or decaying potentials

We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrodinger equations: {-Delta u + v (vertical bar x vertical bar)u - [Delta(u(2))]u = Q(vertical bar x vertical bar)g(u), x is an element of R-N, u(x) -> 0 as vertical bar x vertical bar -> infinity, where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result.