{"paper":{"title":"Positive solutions to singular semilinear elliptic equations with critical potential on cone-like domains","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Sofya Lyakhova, Vitali Liskevich, Vitaly Moroz","submitted_at":"2005-01-02T19:58:17Z","abstract_excerpt":"We study the existence and nonexistence of positive (super-)solutions to a singular semilinear elliptic equation $$-\\nabla\\cdot(|x|^A\\nabla u)-B|x|^{A-2}u=C|x|^{A-\\sigma}u^p$$ in cone--like domains of $\\R^N$ ($N\\ge 2$), for the full range of parameters $A,B,\\sigma,p\\in\\R$ and $C>0$. We provide a complete characterization of the set of $(p,\\sigma)\\in\\R^2$ such that the equation has no positive (super-)solutions, depending on the values of $A,B$ and the principle Dirichlet eigenvalue of the cross--section of the cone.\n  The proofs are based on the explicit construction of appropriate barriers an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501025","kind":"arxiv","version":1},"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"}