{"paper":{"title":"Asymptotic profiles for Choquard equations with general critical nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shiwang Ma, Xiaonan Liu, Yachen Wang","submitted_at":"2024-05-12T03:36:47Z","abstract_excerpt":"In this paper, we study asymptotic behavior of positive ground state solutions for the nonlinear Choquard equation: \\begin{equation}\\label{0.1} -\\Delta u+\\varepsilon u=\\big(I_{\\alpha}\\ast F(u)\\big)F'(u),\\quad u\\in H^1(\\mathbb R^N), \\end{equation} where $F(u)=|u|^{\\frac{N+\\alpha}{N-2}}+G(u)$, $N\\geq3$ is an integer, $I_{\\alpha}$ is the Riesz potential of order $\\alpha\\in(0,N)$, and $\\varepsilon>0$ is a parameter. Under some mild subcritical growth assumptions on $G(u)$, we show that as $\\varepsilon \\to \\infty$, the ground state solutions of \\eqref{0.1}, after a suitable rescaling, converge to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.07149","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/2405.07149/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"}