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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 $\\Omega$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.5875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-21T14:03:17Z","cross_cats_sorted":[],"title_canon_sha256":"ff8f149060d0012c39c55c87078e28806b47d7d878be422b3ff7e02a50cc6f56","abstract_canon_sha256":"2906c9697640abb15f5ed4fc4f9d7cc122cb91e968f4635705b8569719f4eeb2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:19.651508Z","signature_b64":"LBeygW7iBQw9rk/nEPqaKHiteaEb0KxSRiO7m46FJDUJDn/yAIB6i50W8mvZI4hsvGfIx0cYI4H3+ZAYzZnJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a776aed16804603e3cb8582f23c3744125e1e52eb50d35fa651bf4337dc3147b","last_reissued_at":"2026-05-18T02:20:19.650946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:19.650946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\alpha,\\gamma>0$. 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