Some applications of the Nehari manifold method to functionals in C1(X \ {0})

Abstract

Given a real Banach space X, we show that the Nehari manifold method can be applied to functionals which are in . In particular we deal with functionals that can be unbounded near 0, and prove the existence of a ground state and infinitely many critical points for such functionals. These results are then applied to three classes of problems: the prescribed energy problem for a family of functionals depending on a parameter, problems involving the affine p-Laplacian operator, and degenerate Kirchhoff type problems.