Local minimizers for a class of functionals over the Nehari set

Abstract

We analyze the behavior of indefinite type functionals depending on a real parameter λover its Nehari set. A special attention is paid to the extremal parameter λ∗, which plays an important role. The main difficulty arises when λ >λ∗, 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.