{"paper":{"title":"On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mousomi Bhakta, Phuoc-Tai Nguyen","submitted_at":"2018-09-21T01:31:47Z","abstract_excerpt":"We study positive solutions to the fractional Lane-Emden system \\begin{equation*} \\tag{S}\\label{S} \\left\\{ \\begin{aligned} (-\\Delta)^s u &= v^p+\\mu \\quad &&\\text{in } \\Omega \\\\ (-\\Delta)^s v &= u^q+\\nu \\quad &&\\text{in } \\Omega\\\\ u = v &= 0 \\quad &&\\text{in } \\Omega^c={\\mathbb R}^N \\setminus \\Omega, \\end{aligned} \\right. \\end{equation*} where $\\Omega$ is a $C^2$ bounded domains in ${\\mathbb R}^N$, $s\\in(0,1)$, $N>2s$, $p>0$, $q>0$ and $\\mu,\\, \\nu$ are positive measures in $\\Omega$. We prove the existence of the minimal positive solution of the above system under a smallness condition on the to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07909","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"}