{"paper":{"title":"Homogenization of Fucik eigenvalues by optimal partition methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel M. Salort","submitted_at":"2016-01-25T20:23:31Z","abstract_excerpt":"Given a bounded domain $\\Omega$ in $\\mathbb{R}^N$, $N\\geq 1$ we study the asymptotic behavior as $\\varepsilon \\to 0$ of the eigencurves of $$\n  -\\Delta_p u_\\varepsilon=\\alpha_\\varepsilon m(\\tfrac{x}{\\varepsilon})(u_\\varepsilon^+ )^{p-1} - \\beta_\\varepsilon n(\\tfrac{x}{\\varepsilon})(u_\\varepsilon^- )^{p-1} \\quad \\textrm{ in } \\Omega $$ with Dirichlet boundary conditions, where $m$ and $n$ are bounded periodic weights. In this work we obtain accurate bounds of the convergence rates of these curves to some limit curves as $\\varepsilon \\to 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06753","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"}