{"paper":{"title":"Eigenvalues of Sturm-Liouville Operators with Distributional Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Guoliang Shi, Jia Zhao, Jun Yan","submitted_at":"2017-11-19T15:45:29Z","abstract_excerpt":"We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \\begin{equation*} Ly=\\frac{1}{r}\\left( -(p\\left[ y^{\\prime }+sy\\right] )^{\\prime }+sp\\left[ y^{\\prime }+sy\\right] +qy\\right) \\end{equation*} which is based on norm resolvent convergence of classical Sturm-Liouville operators. This enables us to describe the continuous dependence of the $n$-th eigenvalue on the space of self-adjoint boundary conditions and the coefficients of the differential equation after giving the inequalities among the eigenvalues. Moreov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07032","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"}