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In the subcritical case: $1<p<N/(N-2)$ if $N\\ge3$, $1<p<+\\infty$ if $N=2$, we employ the Schauder fixed-point theorem to derive a sequence of positive isolated singular solutions for the abo"},"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":"1708.03041","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-08-10T00:44:07Z","cross_cats_sorted":[],"title_canon_sha256":"ba2dec50f2db1b88a3af22f7e37fbd5319633194472d3fa03dcf7d6c6a9b4a95","abstract_canon_sha256":"a2c712f3068ec902b5bbe176cc8c6a82dbce8d8373077a22d191231b4114acb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:15.114547Z","signature_b64":"7GjE6j4d+XfKSxV0SDJyLj8VH1o6eZWhJmLZg+BloZFpTW2lfmMk7LvT/ysNsNh+lQdp0E6YK0UL8vmhC44SDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe5cd67f531f75ad49f6f6e0c04351c8210e56458e10aa687fb3c7fbf150758","last_reissued_at":"2026-05-18T00:38:15.113897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:15.113897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On isolated singularities of Kirchhoff--type Laplacian problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Binlin Zhang, Huyuan Chen, Mouhamed Moustapha Fall","submitted_at":"2017-08-10T00:44:07Z","abstract_excerpt":"In this paper, we study isolated singular positive solutions for the following Kirchhoff--type Laplacian problem: \\begin{equation*} -\\left(\\theta+\\int_{\\Omega} |\\nabla u| dx\\right)\\Delta u =u^p \\quad{\\rm in}\\quad \\Omega\\setminus \\{0\\},\\qquad u=0\\quad {\\rm on}\\quad \\partial \\Omega, \\end{equation*} where $p>1$, $\\theta\\in \\R$, $\\Omega$ is a bounded smooth domain containing the origin in $\\R^N$ with $N\\ge 2$. 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