Existence of ground states for a modified nonlinear Schrodinger equation

Abstract

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