{"paper":{"title":"A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi","submitted_at":"2024-02-27T12:59:52Z","abstract_excerpt":"We consider the boundary value problem $$\n  \\cases{\n  -\\Delta_\\gamma u = \\lambda u + \\left\\vert u \\right\\vert^{2^*_\\gamma-2}u &in $\\Omega$\\cr\n  u = 0 &on $\\partial\\Omega$,\\cr }\n$$ where $\\Omega$ is an open bounded domain in $\\mathbb{R}^N$, $N \\geq 3$, while $\\Delta_\\gamma$ is the Grushin operator $$ \\Delta_ \\gamma u(z) = \\Delta_x u(z) + \\vert x \\vert^{2\\gamma} \\Delta_y u (z) \\quad (\\gamma\\ge 0). $$ We prove a multiplicity and bifurcation result for this problem, extending the results of Cerami, Fortunato and Struwe and of Fiscella, Molica Bisci and Servadei."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.17476","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/2402.17476/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"}