{"paper":{"title":"Normalized solutions to focusing Sobolev critical biharmonic Schr\\\"{o}dinger equation with mixed dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hong-Rui Sun, Jianlun Liu, Ziheng Zhang","submitted_at":"2025-02-04T06:30:43Z","abstract_excerpt":"This paper is concerned with the following focusing biharmonic Schr\\\"{o}dinger equation with mixed dispersion and Sobolev critical growth: $$ \\begin{cases}\n  {\\Delta}^2u-\\Delta u-\\lambda u-\\mu|u|^{p-2}u-|u|^{4^*-2}u=0\\ \\ \\mbox{in}\\ \\mathbb{R}^N, \\\\[0.1cm]\n  \\int_{\\mathbb{R}^N} u^2 dx = c, \\end{cases} \n$$ where $N \\geq 5$, $\\mu,c>0$, $2<p<4^*:=\\frac{2N}{N-4}$ and $\\lambda \\in \\mathbb{R}$ is a Lagrange multiplier. For this problem, under the $L^2$-subcritical perturbation ($2<p<2+\\frac{8}{N}$), we derive the existence and multiplicity of normalized solutions via the truncation technique, concent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02049","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/2502.02049/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"}