Partial minimization over the Nehari set and applications to elliptic equations

We present a general scheme to find variationally characterized critical points of a functional I H → R on a Hilbert space H with hypothesis where the usual Nehari method is not directly applicable. These critical points arise as minima of I over a suitable subset of the associated Nehari set and are obtained with the aid of fibering methods. Moreover, we derive a comparison result with mountain pass critical values. The abstract results will be applied to classes of logarithmic Choquard and nonlinear Schrödinger equations.