{"paper":{"title":"Disconjugacy characterization by means of spectral of $(k,n-k)$ problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Cabada, Lorena Saavedra","submitted_at":"2015-06-09T19:00:47Z","abstract_excerpt":"This paper is devoted to the description of the interval of parameters for which the general linear $n^{\\rm th}$-order equation\n  \\begin{equation}\n  \\label{e-Ln}\n  T_n[M]\\,u(t) \\equiv u^{(n)}(t)+a_1(t)\\, u^{(n-1)}(t)+\\cdots +a_{n-1}(t)\\, u'(t)+(a_{n}(t)+M)\\,u(t)=0 \\,,\\quad t\\in I\\equiv[a,b],\n  \\end{equation}\n  with $a_i\\in C^{n-i}(I)$, is disconjugate on $ I $.\n  Such interval is characterized by the closed to zero eigenvalues of this problem coupled with $(k,n-k)$ boundary conditions, given by\n  \\begin{equation}\n  \\label{e-k-n-k}\n  u(a)=\\cdots=u^{(k-1)}(a)=u(b)=\\cdots=u^{(n-k-1)}(b)=0\\,,\\quad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03043","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"}