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

Abstract

We proceed with the study of the Nehari manifold method for functionals in , where is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimizer followed by a maximizer). Under some additional conditions we show that the Nehari manifold method provides us with the ground state level and two sequences of critical values for these functionals. These results are applied to the class of prescribed energy problems as well as to the concave–convex problem for the affine -Laplacian operator.