  Multiplicity results are proved for solutions both with positive and negative
energy, as well as nonexistence results, of a generalized quasilinear
Schr\"odinger potential free equation in the entire R^N involving a
nonlinearity which combines a power-type term at a critical level with a
subcritical term, both with weights. The equation has been derived from models
of several physical phenomena such as superfluid film in plasma physics as well
as the self-channelling of a high-power ultra-short laser in matter.
  Proof techniques, also in the symmetric setting, are based on variational
tools, including concentration compactness principles, to overcome lack of
compactness, and the use of a change of variable in order to deal with a well
defined functional.
