English

Further applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$

Analysis of PDEs 2025-02-11 v1

Abstract

We proceed with the study of the Nehari manifold method for functionals in C1(X{0})C^1(X \setminus \{0\}), where XX is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimiser followed by a maximiser). 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 {\it prescribed energy problems} as well as to the concave-convex problem for the {\it affine} pp-Laplacian operator.

Keywords

Cite

@article{arxiv.2502.06611,
  title  = {Further applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$},
  author = {Edir J. F. Leite and Humberto Ramos Quoirin and Kaye Silva},
  journal= {arXiv preprint arXiv:2502.06611},
  year   = {2025}
}