{"paper":{"title":"Normalized solutions of quasilinear Schr\\\"odinger equations in the general $L^2$-supercritical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiang Gao, Xiaoyan Zhang","submitted_at":"2026-06-27T08:19:04Z","abstract_excerpt":"This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schr\\\"odinger equation \\begin{equation*} \\begin{aligned}\n  -\\Delta u-u\\Delta u^2 +\\lambda u=h(u) \\quad\\mathrm{in}\\ \\mathbb{R}^{3}, \\end{aligned} \\end{equation*} where $\\lambda$ appears as a Lagrange multiplier, $h$ is a $L^2$-supercritical and Sobolev subcritical nonlinearity. The solutions correspond to critical points of the energy functional subject to the $L^2$-norm constraint $\\int_{\\mathbb{R}^3}|u|^2dx=a^2>0$. Taking into account the Pohozaev manifold and perturbation method, we obtain t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28806","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/2606.28806/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"}