{"paper":{"title":"On positive solutions of the $(p,A)$-Laplacian with a potential in Morrey space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georgios Psaradakis, Yehuda Pinchover","submitted_at":"2015-08-20T11:38:38Z","abstract_excerpt":"We study qualitative positivity properties of quasilinear equations of the form \\[\n  Q'_{A,p,V}[v] := -\\mathrm{div}(|\\nabla v|_A^{p-2}A(x)\\nabla v) + V(x)|v|^{p-2}v =0 \\qquad x\\in\\Omega, \\] where $\\Omega$ is a domain in $\\mathbb{R}^n$, $1<p<\\infty$, $A=(a_{ij})\\in L^\\infty_{\\rm loc}(\\Omega;\\mathbb{R}^{n\\times n})$ is a symmetric and locally uniformly positive definite matrix, $V$ is a real potential in a certain local Morrey space (depending on $p$), and \\[\n  |\\xi|_{A}^{2}:=A(x)\\xi\\cdot\\xi=\\sum_{i,j=1}^n a_{ij}(x)\\xi_i\\xi_j \\qquad x\\in\\Omega ,~\\xi=(\\xi_1,\\ldots,\\xi_n)\\in \\mathbb{R}^n. \\] Our a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04961","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"}