{"paper":{"title":"On Lane-Emden systems with singular nonlinearities and applications to MEMS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Rodrigo Clemente","submitted_at":"2019-01-09T13:30:48Z","abstract_excerpt":"In this paper we analyse the Lane-Emden system \\begin{equation} \\left\\{ \\begin{alignedat}{3} -\\Delta u = & \\, \\frac{\\lambda f(x)}{(1-v)^2} & \\quad \\text{in} & \\quad\\Omega\\\\ -\\Delta v = & \\, \\frac{\\mu g(x)}{(1-u)^2} & \\quad \\text{in} & \\quad\\Omega\\\\ 0\\leq u &, v < 1 & \\quad \\text{in} & \\quad \\Omega\\\\ u = v & = \\, 0 & \\text{on} & \\quad \\partial\\Omega\\\\ \\end{alignedat} \\right.\\tag{$S_{\\lambda, \\mu}$} \\end{equation} where $\\lambda$ and $\\mu$ are positive parameters and $\\Omega$ is a smooth bounded domain of $\\mathbb{R}^N$ $( N \\geq 1)$. Here we prove the existence of a critical curve $\\Gamma$ whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02728","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"}