{"paper":{"title":"On the extreme value of the Nehari manifold method for a class of Schr\\\"{o}dinger equations with indefinite weight functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e Carlos de Albuquerque, Kaye Silva","submitted_at":"2019-07-22T11:31:26Z","abstract_excerpt":"In this work we are concerned with the following class of equations\n  \\[\n  -\\Delta_p u -\\lambda h(x)|u|^{p-2}u=f(x)|u|^{\\gamma-2}u, \\quad \\mbox{in } \\mathbb{R}^N,\n  \\]\n  involving indefinite weight functions. The existence of solution may depend on the parameter $\\lambda$. We analyze the extreme value $\\lambda^{*}$ and study its relation with the Nehari manifold. Our goal is to establish the existence of two solutions when $\\lambda>\\lambda^{*}$. This work extends and complements the results obtained by J. Chabrowski and D.G. Costa [Comm. Partial Differential Equations 33 (2008), 1368--1394]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09240","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"}