{"paper":{"title":"Semilinear elliptic equations with Hardy potential and gradient nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konstantinos Gkikas, Phuoc-Tai Nguyen","submitted_at":"2019-03-26T18:02:18Z","abstract_excerpt":"Let $\\Omega \\subset {\\mathbb R}^N$ ($N \\geq 3$) be a $C^2$ bounded domain and $\\delta$ be the distance to $\\partial \\Omega$. We study positive solutions of equation (E) $-L_\\mu u+ g(|\\nabla u|) = 0$ in $\\Omega$ where $L_\\mu=\\Delta + \\frac{\\mu}{\\delta^2} $, $\\mu \\in (0,\\frac{1}{4}]$ and $g$ is a continuous, nondecreasing function on ${\\mathbb R}_+$. We prove that if $g$ satisfies a singular integral condition then there exists a unique solution of (E) with a prescribed boundary datum $\\nu$. When $g(t)=t^q$ with $q \\in (1,2)$, we show that equation (E) admits a critical exponent $q_\\mu$ (dependi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11090","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"}