Normalized solutions with positive energies for a coercive problem and application to the cubic–quintic nonlinear Schrödinger equation

Abstract

In any dimension [Formula: see text], for given mass [Formula: see text] and when the [Formula: see text] energy functional [Formula: see text] is coercive on the mass constraint [Formula: see text] we are interested in searching for constrained critical points at positive energy levels. Under general conditions on [Formula: see text] and for suitable ranges of the mass, we manage to construct such critical points which appear as a local minimizer or correspond to a mountain pass or a symmetric mountain pass level. In particular, our results shed some light on the cubic–quintic nonlinear Schrödinger equation in [Formula: see text].