{"paper":{"title":"Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity","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":"2017-05-22T15:01:42Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{N}$ ($N\\geq1$) be a bounded and smooth domain and $a:\\Omega\\rightarrow\\mathbb{R}$ be a sign-changing weight satisfying $\\int_{\\Omega}a<0$. We prove the existence of a positive solution $u_{q}$ for the problem $(P_{a,q})$:\n  $-\\Delta u=a(x)u^{q}$ in $\\Omega$, $\\frac{\\partial u}{\\partial\\nu}=0$ on $\\partial\\Omega$,\n  if $q_{0}<q<1$, for some $q_{0}=q_{0}(a)>0$. In doing so, we improve the existence result previously established in [16]. In addition, we provide the asymptotic behavior of $u_{q}$ as $q\\rightarrow1^{-}$. When $\\Omega$ is a ball and $a$ is radial, we gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07791","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"}