{"paper":{"title":"The A Priori Estimate and Existence of the Positive Solution for A Nonlinear System Involving the Fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ran Zhuo, Yan Li","submitted_at":"2020-06-12T17:45:27Z","abstract_excerpt":"In the paper, we consider the fractional elliptic system \\begin{equation*}\\left\\{\\begin{array}{ll} (- \\Delta)^{\\frac{\\alpha_1}{2}}u(x)+\\sum\\limits^n_{i=1}b_i(x)\\frac{\\partial u}{\\partial x_i}+B(x)u(x)=f(x,u,v),& \\mbox { in } \\Omega,\\\\ (- \\Delta)^{\\frac{\\alpha_2}{2}}v(x)+\\sum\\limits^n_{i=1}c_i(x)\\frac{\\partial v}{\\partial x_i}+C(x)v(x)=g(x,u,v),& \\mbox { in } \\Omega,\\\\ u=v=0, & \\mbox { in } \\mathbb{R}^n\\setminus\\Omega, \\end{array} \\right.\\label{a-1.2} \\end{equation*} where $\\Omega$ is a bounded domain with $C^2$ boundary in $\\mathbb{R}^n$ and $n>\\max\\{\\alpha_1,\\alpha_2\\}$. We first utilize the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.07355","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.07355/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}