Existence of ground states for a modified nonlinear Schrodinger equation

In this paper we prove existence of ground state solutions of the modified nonlinear Schrodinger equation: $-Δu+V(x)u-{1/2}u Δu^{2}=|u|^{p-1}u, x \in \R^N, N \geq 3,$ 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.

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