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We study positive solutions of $$ (P)\\qquad -\\Delta u - \\frac{\\mu}{\\delta^2} u = g(x,u) \\text{ in } \\Omega, \\qquad \\text{tr}^*(u)=\\nu. $$ Here $\\text{tr}^*(u)$ denotes the normalized boundary trace of $u$ which was recently introduced by M. Marcus and P. T. Nguyen. We focus on the case $0<\\mu < C_H(\\Omega)$ (the Hardy constant for $\\Omega$) and provide some qualitative pr"},"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":"1510.03803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-13T18:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"3d526ccf13943905a26d6bb4e80e5a31cf28cb98773624f38068f679207c04d7","abstract_canon_sha256":"9cdd976ad30d2b316dceb7ff5cbb6416df3f74ba7a7c732fcda445d5797b92cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:37.699344Z","signature_b64":"NRaL4bPBV3sCKTD8hghnJ5x4x15fMHWo2FCIRoetM2Xok5qw2HuOm9XOfbSXPJhkSHUdD1B6JD3E445Sa9KFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd3a210ed33a58a8b402f3829ea3d377dc82383ba13ec45c81d9f14c829c6f6","last_reissued_at":"2026-05-18T01:28:37.698638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:37.698638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semilinear elliptic equations with Hardy potential and subcritical source term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Phuoc-Tai Nguyen","submitted_at":"2015-10-13T18:06:34Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\mathbb{R}^N$ and $\\delta(x)=\\text{dist}\\,(x,\\partial \\Omega)$. Assume $\\mu>0$, $\\nu$ is a nonnegative finite measure on $\\partial \\Omega$ and $g \\in C(\\Omega \\times \\mathbb{R}_+)$. We study positive solutions of $$ (P)\\qquad -\\Delta u - \\frac{\\mu}{\\delta^2} u = g(x,u) \\text{ in } \\Omega, \\qquad \\text{tr}^*(u)=\\nu. $$ Here $\\text{tr}^*(u)$ denotes the normalized boundary trace of $u$ which was recently introduced by M. Marcus and P. T. Nguyen. 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