{"paper":{"title":"Zero energy critical points of functionals depending on a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Ramos Quoirin, Jefferson Silva, Kaye Silva","submitted_at":"2021-09-02T13:18:56Z","abstract_excerpt":"We investigate zero energy critical points for a class of functionals $\\Phi_\\mu$ defined on a uniformly convex Banach space, and depending on a real parameter $\\mu$. More precisely, we show the existence of a sequence $(\\mu_n)$ such that $\\Phi_{\\mu_n}$ has a pair of critical points $\\pm u_n$ satisfying $\\Phi_{\\mu_n}(\\pm u_n)=0$, for every $n$. In addition, we provide some properties of $\\mu_n$ and $u_n$. This result, which is proved via a fibering map approach (based on the {\\it nonlinear generalized Rayleigh quotient} method \\cite{I1}) combined with the Ljusternik-Schnirelman theory, is then "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.00930","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.00930/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}