{"paper":{"title":"On least energy solutions for a nonlinear Schr\\\"odinger system with $K$-wise interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Giaretto, Nicola Soave","submitted_at":"2025-07-04T11:09:02Z","abstract_excerpt":"In this paper we establish existence and properties of minimal energy solutions for the weakly coupled system $$ \\begin{cases}\n  -\\Delta u_i + \\lambda_i u_i = \\mu_i|u_i|^{Kq-2}u_i + \\beta|u_i|^{q-2}u_i\\prod_{j\\neq i}|u_j|^q & \\text{in }\\mathbb{R}^d, \\qquad\n  u_i \\in H^1(\\mathbb{R}^d), \\end{cases}\\qquad i=1,\\dots, K, $$ characterized by $K$-wise interaction (namely the interaction term involves the product of all the components). We consider both attractive ($\\beta>0$) and repulsive cases ($\\beta<0$), and we give sufficient conditions on $\\beta$ in order to have least energy fully non-trivial s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03480","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/2507.03480/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"}