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

Given a real Banach space X , we show that the Nehari manifold method can be applied to functionals which are C 1 in X \ { 0 } . 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.