{"paper":{"title":"Bifurcation and multiplicity results for critical Grushin-Choquard problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni Molica Bisci, Pawan Kumar Mishra, Suman Kanungo","submitted_at":"2025-10-15T08:39:51Z","abstract_excerpt":"We consider the following nonlocal Br\\'ezis-Nirenberg type critical Choquard problem involving the Grushin operator\n  \\begin{equation*}\n  \\left\\{\n  \\begin{aligned}\n  -\\Delta_\\gamma & u =\\lambda u + \\left(\\displaystyle\\int_\\Omega \\frac{|u(w)|^{2^*_{\\gamma,\\mu}}}{d(z-w)^\\mu}dw\\right) |u|^{2^*_{\\gamma,\\mu}-2}u \\quad &&\\text{in} \\ \\Omega,\n  u &= 0 \\quad &&\\text{on} \\, \\partial \\Omega,\n  \\end{aligned}\n  \\right.\n  \\end{equation*}\n  where $\\Omega$ is an open bounded domain in $\\mathbb{R}^N$, $N \\geq 3$, with $\\Omega \\cap \\{ x=0\\} \\neq \\emptyset$, and $\\lambda >0$ is a parameter. Here, $\\Delta_\\gamma$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.13299","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.13299/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"}