{"paper":{"title":"Eigenvalues for systems of fractional $p-$Laplacians","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":"2016-05-10T10:24:37Z","abstract_excerpt":"We study the eigenvalue problem for a system of fractional $p-$Laplacians, that is, $$ \\begin{cases}\n  (-\\Delta_p)^r u = \\lambda\\dfrac{\\alpha}p|u|^{\\alpha-2}u|v|^{\\beta} &\\text{in } \\Omega,\\vspace{.1cm}\n  (-\\Delta_p)^s u = \\lambda\\dfrac{\\beta}p|u|^{\\alpha}|v|^{\\beta-2}v &\\text{in } \\Omega,\n  u=v=0 &\\text{in }\\Omega^c=\\R^N\\setminus\\Omega. \n  \\end{cases}\n  $$\n  We show that there is a first (smallest) eigenvalue that is simple and has associated eigen-pairs composed of positive and bounded functions. Moreover, there is a sequence of eigenvalues $\\lambda_n$ such that\n  $\\lambda_n\\to\\infty$ as $n\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02926","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"}