{"paper":{"title":"Existence and convergence of ground state solutions for Choquard-type systems on lattice graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lidan Wang","submitted_at":"2025-07-28T01:49:13Z","abstract_excerpt":"In this paper, we study the $p$-Laplacian system with Choquard-type nonlinearity $$ \\begin{cases}-\\Delta_{p} u+(\\lambda a+1)|u|^{p-2} u=\\frac{1}{\\gamma} \\left(R_\\alpha\\ast F(u,v)\\right)F_{u}(u, v), \\\\ -\\Delta_{p} v+(\\lambda b+1)|v|^{p-2} v=\\frac{1}{\\gamma} \\left(R_\\alpha\\ast F(u,v)\\right)F_{v}(u, v),\\end{cases} $$ on lattice graphs $\\mathbb{Z}^N$, where $\\alpha \\in(0,N),\\,p\\geq 2,\\,\\gamma> \\frac{(N+\\alpha)p}{2N},\\,\\lambda>0$ is a parameter and $R_{\\alpha}$ is the Green's function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some assumptions on the functions $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20464","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/2507.20464/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"}