{"paper":{"title":"The first nontrivial eigenvalue for a system of $p-$Laplacians with Neumann and Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Julio D. Rossi, Leandro M. Del Pezzo","submitted_at":"2015-05-27T17:18:27Z","abstract_excerpt":"We deal with the first eigenvalue for a system of two $p-$Laplacians with Dirichlet and Neumann boundary conditions. If $\\Delta_{p}w=\\mbox{div}(|\\nabla w|^{p-2}w)$ stands for the $p-$Laplacian and $\\frac{\\alpha}{p}+\\frac{\\beta}{q}=1,$ we consider $$ \\begin{cases} -\\Delta_pu= \\lambda \\alpha |u|^{\\alpha-2} u|v|^{\\beta} &\\text{ in }\\Omega,\\\\ -\\Delta_q v= \\lambda \\beta |u|^{\\alpha}|v|^{\\beta-2}v &\\text{ in }\\Omega,\\\\ \\end{cases} $$ with mixed boundary conditions $$ u=0, \\qquad |\\nabla v|^{q-2}\\dfrac{\\partial v}{\\partial \\nu }=0, \\qquad \\text{on }\\partial \\Omega. $$ We show that there is a first no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07403","kind":"arxiv","version":2},"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"}