{"paper":{"title":"On a lower a priori estimate of minimal eigenvalue of one Sturm-Liouville problem with second-type boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A.A. Vladimirov, E.S. Karulina","submitted_at":"2014-12-26T20:29:26Z","abstract_excerpt":"It is proved that for class $A_\\gamma=\\{q\\in L_1[0,1]: q\\geq 0, \\int_0^1 q^\\gamma\\,dx=1\\}$, where $\\gamma\\in (0,1)$, there exists a potential $q_*\\in A_\\gamma$ such that minimal eigenvalue $\\lambda_1(q_*)$ of boundary problem $$ -y\"+q_*y=\\lambda y, y'(0)=y'(1)=0 $$ is equal to $m_\\gamma=\\inf_{q\\in A_\\gamma}\\lambda_1(q)$. The equality $m_\\gamma=1$ for $\\gamma\\leq 1-2\\pi^{-2}$ and the inequality $m_\\gamma<1$ for $\\gamma>1-2\\pi^{-2}$ are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7986","kind":"arxiv","version":2},"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"}