{"paper":{"title":"Minimal energy solutions to the fractional Lane-Emden system, I: Existence and singularity formation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Seunghyeok Kim, Woocheol Choi","submitted_at":"2016-10-10T11:30:11Z","abstract_excerpt":"This is the first of two papers which study asymptotic behavior of minimal energy solutions to the fractional Lane-Emden system in a smooth bounded domain $\\Omega$ \\[(-\\Delta)^s u = v^p, \\quad (-\\Delta)^s v = u^q \\text{ in } \\Omega \\quad \\text{and} \\quad u = v = 0 \\text{ on } \\pa \\Omega \\quad \\text{for } 0 < s < 1\\] under the assumption that the subcritical pair $(p,q)$ approaches to the critical Sobolev hyperbola. If $p = 1$, the above problem is reduced to the subcritical higher-order fractional Lane-Emden equation with the Navier boundary condition \\[(-\\Delta)^s u = u^{\\frac{n+2s}{n-2s}-\\ep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02853","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"}