Abstract

I’ll present results of existence of positive solutions with fixed mass for a class of mass supercritical Schrödinger equations with a negative potential term. I’ll consider two cases: firstly, under a smallness assumption on the potential and no condition on the mass, we find a mountain pass solution at positive energy level; secondly, requiring that the mass is smaller than some bound depending on the potential and that this is not too small in a suitable sense, we find two solutions: a local minimizer with negative energy and a mountain pass solution with positive energy.