{"paper":{"title":"Generalized spectrum of the $\\boldsymbol{(p,2)}$-Laplacian under a parametric boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gustavo Madeira, Jamil Abreu","submitted_at":"2015-07-13T00:45:50Z","abstract_excerpt":"In this paper we study an eigenvalue problem for the so called $(p,2)$-Laplace operator on a smooth bounded domain under a nonlinear Steklov type boundary condition, namely \\begin{equation} \\left\\{ \\begin{aligned} -\\Delta_pu-\\Delta u & =\\lambda a(x)u \\ \\ \\text{in}\\ \\Omega,\\\\ (|\\nabla u|^{p-2}+1)\\dfrac{\\partial u}{\\partial\\nu} & =\\lambda b(x)u \\ \\ \\text{on}\\ \\partial\\Omega . \\end{aligned} \\right. \\end{equation} Under suitable integrability and boundedness assumptions on the positive weight functions $a$ and $b$, we show that, for all $p>1$, the eigenvalue set consists of an isolated null eigenv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03299","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"}