{"paper":{"title":"On Dirichlet problems with singular nonlinearity of indefinite sign","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tom\\'as Godoy, Uriel Kaufmann","submitted_at":"2014-11-21T14:03:17Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\mathbb{R}^{N}$, $N\\geq1$, let $K$, $M$ be two nonnegative functions and let $\\alpha,\\gamma>0$. We study existence and nonexistence of positive solutions for singular problems of the form $-\\Delta u=K\\left( x\\right) u^{-\\alpha}-\\lambda M\\left( x\\right) u^{-\\gamma}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\lambda>0$ is a real parameter. We mention that as a particular case our results apply to problems of the form $-\\Delta u=m\\left( x\\right) u^{-\\gamma}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $m$ is allowed to change sign in $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5875","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"}