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We use variational methods to show the existence and multiplicity of positive solutions of above problem with respect to parameter $\\la$."},"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":"1602.00872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-02T10:50:30Z","cross_cats_sorted":[],"title_canon_sha256":"00da368bba9ae20315f8e96d19053e44f79c297ea2c4d6bbfc2c1590d07255d7","abstract_canon_sha256":"37be0e795a893187fd9d6b5e7ff0f95b6cd95ee1f44670c0595511071e1779c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:51.212504Z","signature_b64":"/rHJQnXxeYKcoPd9lIvNhqn4sfxl+dZ7WtPQktdDRUypXiqaJzc9iaQ4GxLjLwMvsS9OrqhqFV8+5PdQSoEyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0197769918d2be904c12f7d28adb573e7749237c7a8644d098366b597f80112a","last_reissued_at":"2026-05-18T01:15:51.211958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:51.211958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Dirichlet problem for fractional $p$-Laplacian with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K.Sreenadh, Tuhina Mukherjee","submitted_at":"2016-02-02T10:50:30Z","abstract_excerpt":"In this article, we study the following fractional $p$-Laplacian equation with critical growth singular nonlinearity \\begin{equation*}\n  \\quad (-\\De_{p})^s u = \\la u^{-q} + u^{\\alpha}, u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om. \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > sp, s \\in (0,1), \\la >0, 0 < q \\leq 1 $ and $\\alpha\\le p^*_s-1$. We use variational methods to show the existence and multiplicity of positive solutions of above problem with respect to parameter $\\la$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00872","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.00872","created_at":"2026-05-18T01:15:51.212047+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.00872v2","created_at":"2026-05-18T01:15:51.212047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00872","created_at":"2026-05-18T01:15:51.212047+00:00"},{"alias_kind":"pith_short_12","alias_value":"AGLXNGIY2K7J","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AGLXNGIY2K7JATAS","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AGLXNGIY","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ","json":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ.json","graph_json":"https://pith.science/api/pith-number/AGLXNGIY2K7JATAS67JIVW2XHZ/graph.json","events_json":"https://pith.science/api/pith-number/AGLXNGIY2K7JATAS67JIVW2XHZ/events.json","paper":"https://pith.science/paper/AGLXNGIY"},"agent_actions":{"view_html":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ","download_json":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ.json","view_paper":"https://pith.science/paper/AGLXNGIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.00872&json=true","fetch_graph":"https://pith.science/api/pith-number/AGLXNGIY2K7JATAS67JIVW2XHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/AGLXNGIY2K7JATAS67JIVW2XHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ/action/storage_attestation","attest_author":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ/action/author_attestation","sign_citation":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ/action/citation_signature","submit_replication":"https://pith.science/pith/AGLXNGIY2K7JATAS67JIVW2XHZ/action/replication_record"}},"created_at":"2026-05-18T01:15:51.212047+00:00","updated_at":"2026-05-18T01:15:51.212047+00:00"}