  In this paper we prove existence of ground state solutions of the modified
nonlinear Schrodinger equation: $$ -\Delta u+V(x)u-{1/2}u \Delta
u^{2}=|u|^{p-1}u, x \in \R^N, N \geq 3, $$ under some hypotheses on $V(x)$.
This model has been proposed in the theory of superfluid films in plasma
physics. As a main novelty with respect to some previous results, we are able
to deal with exponents $p\in(1,3)$. The proof is accomplished by minimization
under a convenient constraint.
