{"paper":{"title":"Dependence of Solutions and Eigenvalues of Third Order Linear Measure Differential Equations on Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Guoliang Shi, Jun Yan, Yixuan Liu","submitted_at":"2019-01-03T07:36:15Z","abstract_excerpt":"This paper deals with a complex third order linear measure differential equation \\begin{equation*} i\\mathrm{d}\\left( y^{\\prime }\\right) ^{\\bullet }+2iq\\left( x\\right) y^{\\prime }\\mathrm{d}x+y\\left( i\\mathrm{d}q\\left( x\\right) +\\mathrm{d}p\\left( x\\right) \\right) = \\lambda y\\mathrm{d}x \\end{equation*} on a bounded interval with boundary conditions presenting a mixed aspect of the Dirichlet and the periodic problems. The dependence of eigenvalues on the coefficients $p$, $q$ is investigated. We prove that the $n$-th eigenvalue is continuous in $p$, $q$ when the norm topology of total variation an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00638","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"}