{"paper":{"title":"Existence and Multiplicity for elliptic p-Laplacian problems with critical growth in the gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio J. Fern\\'andez, Colette De Coster","submitted_at":"2018-01-12T12:59:50Z","abstract_excerpt":"We consider the boundary value problem $-\\Delta_p u = \\lambda c(x) |u|^{p-2}u + \\mu(x) |\\grad u|^p + h(x)$, $u \\in W^{1,p}_0(\\Omega) \\cap L^{\\infty}(\\Omega)$, where $\\Omega \\subset \\mathbb R^N$, $N \\geq 2$, is a bounded domain with smooth boundary. We assume $c$, $h \\in L^q(\\Omega)$ for some $q > \\max\\{N/p,1\\}$ with $c \\gneqq 0$ and $\\mu \\in L^{\\infty}(\\Omega)$. We prove existence and uniqueness results in the coercive case $ \\lambda \\leq 0$ and existence and multiplicity results in the non-coercive case $ \\lambda >0$. Also, considering stronger assumptions on the coefficients, we clarify the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04155","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"}