{"paper":{"title":"A critical phenomenon for sublinear elliptic equations in cone-like domains","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Vitali Liskevich, Vitaly Moroz, Vladimir Kondratiev, Zeev Sobol","submitted_at":"2003-07-12T18:04:22Z","abstract_excerpt":"We study positive supersolutions to an elliptic equation $(*)$: $-\\Delta u=c|x|^{-s}u^p$, $p,s\\in\\bf R$ in cone-like domains in $\\bf R^N$ ($N\\ge 2$). We prove that in the sublinear case $p<1$ there exists a critical exponent $p_*<1$ such that equation $(*)$ has a positive supersolution if and only if $-\\infty<p<p_*$. The value of $p_*$ is determined explicitly by $s$ and the geometry of the cone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307183","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"}