{"paper":{"title":"Normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Ji, Zhentao He","submitted_at":"2025-05-21T04:46:36Z","abstract_excerpt":"In this paper, we study the following nonlinear Dirac equations (NLDE) on noncompact metric graph $\\mathcal{G}$ with localized nonlinearities \\begin{equation} \\mathcal{D} u - \\omega u= a\\chi_{\\mathcal{K}}|u|^{p-2}u, \\end{equation} where $\\mathcal{D}$ is the Dirac operator on $\\mathcal{G}$, $u: \\mathcal{G} \\to \\mathbb{C}^2$, $\\omega\\in \\mathbb{R}$, $a > 0$, $\\chi_{\\mathcal{K}}$ is the characteristic function of the compact core $\\mathcal{K}$, and $p>2$. First, for $2<p<4$, we prove the existence of normalized solutions to (NLDE) using a perturbation argument. Then, for $p \\geq 4$, we establish "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15100","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/2505.15100/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"}