{"paper":{"title":"Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator","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":"2025-01-19T11:14:12Z","abstract_excerpt":"In this article we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator $\\Delta_\\gamma^p$. We extend to a generic $p>1$ a result which was proved only when $p=2$. When $p\\neq 2$, the nonlinear operator $-\\Delta_\\gamma^p$ has no linear eigenspaces, so our extension is nontrivial and requires an abstract critical theorem which is not based on linear subspaces. We also prove a new abstract result based on a pseudo-index related to the $\\mathbf{Z}_2$-cohomological index that is applicable here. We provide a version of the Lions' Concentration"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11013","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/2501.11013/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"}