{"paper":{"title":"Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marius Ghergu, Steven D. Taliaferro","submitted_at":"2014-07-16T22:28:11Z","abstract_excerpt":"We study the behavior near the origin of $C^2$ positive solutions $u(x)$ and $v(x)$ of the system\n  $0\\le -\\Delta u \\le (\\frac{1}{|x|^\\alpha}* v)^\\lambda$\n  $0\\le -\\Delta v \\le (\\frac{1}{|x|^\\beta}* u)^\\sigma$\n  in $B_2(0)\\setminus\\{0\\} \\subset R^n$, $n\\ge 3$, where $\\lambda,\\sigma \\ge 0$ and $\\alpha,\\beta\\in (0,n)$.\n  A by-product of our methods used to study these solutions will be results on the behavior near the origin of $L^1(B_1(0))$ solutions $f$ and $g$ of the system\n  $0 \\le f(x) \\le C(|x|^{2-\\alpha} + \\int_{|y|<1}\\frac{ g(y) dy}{|x-y|^{\\alpha-2}} )^\\lambda$\n  $0 \\le g(x) \\le C(|x|^{2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4517","kind":"arxiv","version":2},"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"}