Further applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929707235147776 |
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| author | Leite, Edir J. F. Quoirin, Humberto Ramos Silva, Kaye |
| author_facet | Leite, Edir J. F. Quoirin, Humberto Ramos Silva, Kaye |
| contents | We proceed with the study of the Nehari manifold method for functionals in $C^1(X \setminus \{0\})$, where $X$ 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} $p$-Laplacian operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Further applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ Leite, Edir J. F. Quoirin, Humberto Ramos Silva, Kaye Analysis of PDEs We proceed with the study of the Nehari manifold method for functionals in $C^1(X \setminus \{0\})$, where $X$ 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} $p$-Laplacian operator. |
| title | Further applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.06611 |