{"paper":{"title":"A curve of positive solutions for an indefinite sublinear Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Ramos Quoirin, Kenichiro Umezu, Uriel Kaufmann","submitted_at":"2017-09-14T14:50:39Z","abstract_excerpt":"We investigate the existence of a curve $q\\mapsto u_{q}$, with $q\\in(0,1)$, of positive solutions for the problem $(P_{a,q})$: $-\\Delta u=a(x)u^{q}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\Omega$ is a bounded and smooth domain of $\\mathbb{R}^{N}$ and $a:\\Omega\\rightarrow\\mathbb{R}$ is a sign-changing function (in which case the strong maximum principle does not hold). In addition, we analyze the asymptotic behavior of $u_{q}$ as $q\\rightarrow0^{+}$ and $q\\rightarrow1^{-}$. We also show that in some cases $u_{q}$ is the ground state solution of $(P_{a,q})$. As a byproduct, we obtain exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04822","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"}