{"paper":{"title":"Spiked solutions for Schr\\\"odinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Hugo Tavares","submitted_at":"2016-05-12T12:00:43Z","abstract_excerpt":"In this paper we deal with the nonlinear Schr\\\"odinger system \\[ -\\Delta u_i =\\mu_i u_i^3 + \\beta u_i \\sum_{j\\neq i} u_j^2 + \\lambda_i u_i, \\qquad u_1,\\ldots, u_m\\in H^1_0(\\Omega) \\] in dimension 4, a problem with critical Sobolev exponent. In the competitive case ($\\beta<0$ fixed or $\\beta\\to -\\infty$) or in the weakly cooperative case ($\\beta\\geq 0$ small), we construct, under suitable assumptions on the Robin function associated to the domain $\\Omega$, families of positive solutions which blowup and concentrate at different points as $\\lambda_1,\\ldots, \\lambda_m\\to 0$. This problem can be s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03776","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"}