{"paper":{"title":"Nonlocal refuge model with a partial control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jerome Coville (BIOSP)","submitted_at":"2013-05-30T14:16:37Z","abstract_excerpt":"In this paper, we analyse the structure of the set of positive solutions of an heterogeneous nonlocal equation of the form: $$ \\int_{\\Omega} K(x, y)u(y)\\,dy -\\int_ {\\Omega}K(y, x)u(x)\\, dy + a_0u+\\lambda a_1(x)u -\\beta(x)u^p=0 \\quad \\text{in}\\quad \\times \\O$$ where $\\Omega\\subset \\R^n$ is a bounded open set, $K\\in C(\\R^n\\times \\R^n) $ is nonnegative, $a_i,\\beta \\in C(\\Omega)$ and $\\lambda\\in\\R$. Such type of equation appears in some studies of population dynamics where the above solutions are the stationary states of the dynamic of a spatially structured population evolving in a heterogeneous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7122","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"}