{"paper":{"title":"Elliptic equations involving the $p$-Laplacian and a gradient term having natural growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Djairo G. de Figueiredo, Humberto Ramos Quoirin, Jean-Pierre Gossez, Pedro Ubilla","submitted_at":"2017-01-09T12:01:31Z","abstract_excerpt":"We investigate the problem $$ \\left\\{ \\begin{array}{ll} -\\Delta_p u = g(u)|\\nabla u|^p + f(x,u) \\ & \\mbox{in} \\ \\ \\Omega, \\ \\ \\\\ u>0 \\ &\\mbox{in} \\ \\ \\Omega, \\ \\\n  u = 0 \\ &\\mbox{on} \\ \\ \\partial\\Omega, \\end{array}\n  \\right. \\leqno{(P)} $$ in a bounded smooth domain $\\Omega \\subset \\mathbb{R}^N$. Using a Kazdan-Kramer change of variable we reduce this problem to a quasilinear one without gradient term and therefore approachable by variational methods. In this way we come to some new and interesting problems for quasilinear elliptic equations which are motivated by the need to solve $(P)$. Amon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02148","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"}