{"paper":{"title":"On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Yavdat Il'yasov","submitted_at":"2015-09-26T19:20:08Z","abstract_excerpt":"We study applicability conditions of the Nehari manifold method for the equation of the form $ D_u T(u)-\\lambda D_u F(u)=0 $ in a Banach space $W$, where $\\lambda$ is a real parameter. Our study is based on the development of the theory Rayleigh's quotient for nonlinear problems. It turns out that the extreme values of parameter $\\lambda$ for the Nehari manifold method can be found through the critical values of a corresponding nonlinear generalized Rayleigh's quotient. In the main part of the paper, we provide some general results on this relationship. Applications are given to several types "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08019","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}