{"paper":{"title":"On the second minimax level for the scalar field equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril Tintarev, Kanishka Perera","submitted_at":"2012-08-06T11:42:08Z","abstract_excerpt":"The paper studies eigenfunctions for the scalar field equation on $\\R^N$ at the second minimax level $\\lambda_2$. Similarly to the well-studied case of the ground state, there is a threshold level $\\lambda^#$ such that $\\lambda_2\\le \\lambda^#$, and a critical point at the level $\\lambda_2$ exists if the inequality is strict. Unlike the case of the ground state, the level $\\lambda_2$ is not attained in autonomous problems, and the existence is shown when the potential near infinity approaches the constant level from below not faster than $e^{- \\varepsilon |x|}$. The paper also considers questio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1139","kind":"arxiv","version":3},"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"}