{"paper":{"title":"Normalized solutions and stability for biharmonic Schr\\\"odinger equation with potential on waveguide manifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Wang, Zhaoyang Yin","submitted_at":"2024-09-20T09:14:04Z","abstract_excerpt":"In this paper, we study the following biharmonic Schr\\\"odinger equation with potential and mixed nonlinearities \\begin{equation*}\n  \\left\\{\\begin{array}{ll}\\Delta^2 u +V(x,y)u+\\lambda u =\\mu|u|^{p-2}u+|u|^{q-2}u,\\ (x, y) \\in \\Omega_r \\times \\mathbb{T}^n, \\\\ \\int_{\\Omega_r\\times\\mathbb{T}^n}u^2dxdy=\\Theta,\\end{array} \\right. \\end{equation*} where $\\Omega_r \\subset \\mathbb{R}^d$ is an open bounded convex domain, $r>0$ is large and $\\mu\\in\\mathbb{R}$. The exponents satisfy $2<p<2+\\frac{8}{d+n}<q<4^*=\\frac{2(d+n)}{d+n-4}$, so that the nonlinearity is a combination of a mass subcritical and a mass "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00032","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/2410.00032/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"}