{"paper":{"title":"Half eigenvalues and the Fucik spectrum of multi-point, boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bryan P. Rynne, Francois Genoud","submitted_at":"2011-10-04T15:01:59Z","abstract_excerpt":"We consider the nonlinear boundary value problem consisting of the equation\n\\tag{1} -u\" = f(u) + h, \\quad \\text{a.e. on $(-1,1)$,}\nwhere $h \\in L^1(-1,1)$, together with the multi-point, Dirichlet-type boundary conditions\n\\tag{2} u(\\pm 1) = \\sum^{m^\\pm}_{i=1}\\alpha^\\pm_i u(\\eta^\\pm_i)\nwhere $m^\\pm \\ge 1$ are integers, $\\alpha^\\pm = (\\alpha_1^\\pm, ...,\\alpha_m^\\pm) \\in [0,1)^{m^\\pm}$, $\\eta^\\pm \\in (-1,1)^{m^\\pm}$, and we suppose that $$\n  \\sum_{i=1}^{m^\\pm} \\alpha_i^\\pm < 1 . $$ We also suppose that $f : \\mathbb{R} \\to \\mathbb{R}$ is continuous, and $$ 0 < f_{\\pm\\infty}:=\\lim_{s \\to \\pm\\infty}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0712","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"}