{"paper":{"title":"Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Catherine Bandle, Moshe Marcus, Vitaly Moroz","submitted_at":"2016-04-29T13:45:31Z","abstract_excerpt":"We study a nonlinear equation in the half-space $\\{x_1>0\\}$ with a Hardy potential, specifically \\[-\\Delta u -\\frac{\\mu}{x_1^2}u+u^p=0\\quad\\text{in}\\quad \\mathbb R^n_+,\\] where $p>1$ and $-\\infty<\\mu<1/4$. The admissible boundary behavior of the positive solutions is either $O(x_1^{-2/(p-1)})$ as $x_1\\to 0$, or is determined by the solutions of the linear problem $-\\Delta h -\\frac{\\mu}{x_1^2}h=0$. In the first part we study in full detail the separable solutions of the linear equations for the whole range of $\\mu$. In the second part, by means of sub and supersolutions we construct separable s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08830","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"}