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

2024/09/08 by Leite, Edir Junior Ferreira, Quoirin, Humberto Ramos, Silva, Kaye
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.05138

Abstract

Given a real Banach space X, we show that the Nehari manifold method can be applied to functionals which are C¹ 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 \it prescribed energy problem for a family of functionals depending on a parameter, problems involving the \it affine p-Laplacian operator, and degenerate Kirchhoff type problems.

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