{"paper":{"title":"Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Vitali Liskevich, Vitaly Moroz, Vladimir Kondratiev","submitted_at":"2003-07-10T10:47:12Z","abstract_excerpt":"We study the problem of the existence and nonexistence of positive solutions to a superlinear second-order divergence type elliptic equation with measurable coefficients $(*)$: $-\\nabla\\cdot a\\cdot\\nabla u=u^p$ in an unbounded cone--like domain $G\\subset\\bf R^N$ $(N\\ge 3)$. We prove that the critical exponent $p^*(a,G)=\\inf\\{p>1 : (*) \\hbox{has a positive supersolution in} G\\}$ for a nontrivial cone-like domain is always in $(1,N/(N-2))$ and in contrast with exterior domains depends both on the geometry of the domain $G$ and the coefficients $a$ of the equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307144","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"}