{"paper":{"title":"The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lidan Wang, Ruowei Li","submitted_at":"2022-07-30T14:41:27Z","abstract_excerpt":"In this paper, we study the nonlinear Choquard equation \\begin{eqnarray*} \\Delta^{2}u-\\Delta u+(1+\\lambda a(x))u=(R_{\\alpha}\\ast|u|^{p})|u|^{p-2}u \\end{eqnarray*} on a Cayley graph of a discrete group of polynomial growth with the homogeneous dimension $N\\geq 2$, where $\\alpha\\in(0,N),\\,p>\\frac{N+\\alpha}{N},\\,\\lambda$ is a positive parameter and $R_\\alpha$ stands for the Green's function of the discrete fractional Laplacian, which has same asymptotics as the Riesz potential. Under some assumptions on $a(x)$, we establish the existence and asymptotic behavior of ground state solutions for the n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.00236","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/2208.00236/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"}