{"paper":{"title":"On majorants of eigenvalues of Sturm-Liouville problems with potentials from balls of weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A.A. Vladimirov","submitted_at":"2014-12-26T21:19:11Z","abstract_excerpt":"It is constructively proved that for class $A_{r,\\gamma}=\\{q\\in L_{1,loc}(0,1): q\\leq 0, \\int_0^1 rq^\\gamma\\,dx\\leqslant 1\\}$, where $r\\in C[0,1]$ is uniformly positive weight and $\\gamma>1$, there exists a unique potential $\\hat q\\in A_{r,\\gamma}$ such that minimal eigenvalue $\\lambda_0(\\hat q)$ of boundary problem $$-y\"+\\hat qy=\\lambda y, y(0)=y(1)=0 $$ is equal to $M_{r,\\gamma}=\\sup_{q\\in A_{r,\\gamma}}\\lambda_0(q)$. For case $\\gamma=1$ we obtain that there exists a unique potential $\\hat q\\in\\Gamma_{r,\\gamma}$ with analogous property. Here $\\Gamma_{r,\\gamma}$ is a closure of $A_{r,\\gamma}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7992","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"}