{"paper":{"title":"Critical quasi-linear Schr\\\"{o}dinger system with $p$-Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Neng cheng, Wei Dai, Zhao Liu","submitted_at":"2026-06-09T09:33:28Z","abstract_excerpt":"In this paper, we mainly consider positive solution to the $D^{1,p}(\\R^{N})$-critical quasi-linear Schr\\\"{o}dinger system with $p$-Laplacian: \\begin{equation*}\\begin{cases} -\\Delta_p u = u^{\\alpha}v^{\\beta} \\, \\ \\ \\ \\ \\ \\text{in}\\,\\ \\ \\R^N, \\\\ -\\Delta_p v = u^{\\beta}v^{\\alpha} \\,\\ \\ \\ \\ \\ \\text{in}\\,\\ \\ \\R^N, \\end{cases}\\end{equation*} where $1<p<N$, $N\\geq2$, $0\\leq \\alpha \\leq \\beta,$ and $u,v\\in D^{1,p}(\\R^N)$. We establish regularity and the sharp estimates on asymptotic behaviors for any positive solution $(u,v)$. Then, we prove that all positive solutions are radially symmetric and stric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10630","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/2606.10630/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"}