{"paper":{"title":"Normalized groundstates for mixed $(p,2)$-Laplacian equations in $\\mathbb R^2$ with exponential critical growth","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Zhong, Jiankang Xia","submitted_at":"2026-05-19T15:02:54Z","abstract_excerpt":"We investigate normalized groundstates for mixed $(p,2)$-Laplacian equations \\begin{align*}\n  \\begin{cases}\n  -\\Delta_p u-\\Delta u+\\lambda u=f(u) & \\text{in } \\mathbb{R}^2,\n  \\displaystyle \\int_{\\mathbb{R}^2}|u|^2\\,\\mathrm{d}x=m,\n  u\\in H^1(\\mathbb{R}^2)\\cap D^{1,p}(\\mathbb{R}^2),\n  \\end{cases} \\end{align*} where $\\Delta_p$ denotes the $p$-Laplacian with $1<p<2$, $\\lambda\\in\\mathbb{R}$ represents a Lagrange multiplier and the nonlinerity $f$ exhibits exponential critical growth. Compared to the single-Laplacian case, the lack of regularity here precludes the Pohozaev identity, and the exponent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19946","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/2605.19946/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"}