{"paper":{"title":"The eigenvalue Characterization for the constant Sign Green's Functions 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":"2015-04-09T09:31:42Z","abstract_excerpt":"This paper is devoted to the study of the sign of the Green's function related to a general linear $n^{\\rm th}$-order operator, depending on a real parameter, $T_n[M]$, coupled with the $(k,n-k)$ boundary value conditions.\n  If operator $T_n[\\bar M]$ is disconjugate for a given $\\bar M$, we describe the interval of values on the real parameter $M$ for which the Green's function has constant sign.\n  One of the extremes of the interval is given by the first eigenvalue of operator $T_n[\\bar M]$ satisfying $(k,n-k)$ conditions.\n  The other extreme is related to the minimum (maximum) of the first e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02229","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"}