Quasilinear Schrödinger equations involving concave and convex nonlinearities

In this paper the mountain--pass theorem and the Ekeland variational principle in a suitable Orlicz space are employed to establish the existence of positive standing wave solutions for a quasilinear Schrodinger equation involving a combination of concave and convex terms. The second order nonlinearity considered in this paper corresponds to the superfluid equation in plasma physics.