Multiplicity results for generalized quasilinear critical Schrödinger equations in $${\mathbb {R}}^N$$

Abstract

AbstractMultiplicity results are proved for solutions both with positive and negative energy, as well as nonexistence results, of a generalized quasilinear Schrödinger potential free equation in the entire $${\mathbb {R}}^N$$ 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.