{"paper":{"title":"Radial symmetry and sharp asymptotic behaviors of nonnegative solutions to weighted doubly $D^{1,p}$-critical quasi-linear nonlocal elliptic equations with Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daomin Cao, Wei Dai, Yafei Li","submitted_at":"2025-02-09T10:20:53Z","abstract_excerpt":"In this paper, we mainly consider nonnegative weak solutions $u\\in D^{1,p}(\\R^{N})$ to the doubly $D^{1,p}(\\R^{N})$-critical nonlocal quasi-linear Schr\\\"{o}dinger-Hartree equation: \\begin{align*} -\\Delta_p u- \\mu \\frac{u^{p-1}}{|x|^p}=\\left(|x|^{-2p}\\ast |u|^{p}\\right)|u|^{p-2}u \\qquad &\\mbox{in} \\,\\, \\mathbb{R}^N, \\end{align*} where $N\\geq3$, $0\\leq\\mu< \\bar{\\mu}:=\\left( (N-p)/p \\right)^p$ and $1<p<\\frac{N}{2}$. When $\\mu>0$, due to appearance of the Hardy potential, the equation has singularity at $0\\in\\mathbb{R}^{N}$ and hence is not translation invariant, so sharp asymptotic estimates near"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07816","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/2502.07816/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"}