  We analyze the topological structure of the Nehari set for a class of
functionals depending on a real parameter $\lambda$, and having two degrees of
homogeneity. A special attention is paid to the extremal parameter $\lambda^*$,
which is the threshold value for the Nehari set to be given by a {\it natural
constraint}. The main difficulty arises when $\lambda>\lambda^*$, as the energy
functional may be unbounded from below over the Nehari set. In such situation
we prove the existence of local minimizers of the functional constrained to
this set. We unify and extend previous existence and multiplicity results for
critical points of indefinite, $(p,q)$-Laplacian, and Kirchhoff type problems.
