{"paper":{"title":"Existence of non-radial entire solutions for the H\\'enon equation beyond even exponents","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Qinfeng Jiang","submitted_at":"2026-06-30T13:51:03Z","abstract_excerpt":"This paper is concerned with the existence of non-radial positive classical solutions for the critical H\\'enon equation \\[ -\\Delta u=|x|^\\alpha u^{\\frac{N+2+2\\alpha}{N-2}} \\qquad \\text{in }\\mathbb R^N, \\] where \\(\\alpha>0\\) and \\(N\\ge3\\), satisfying the Newtonian-type decay condition at infinity.\n  Gladiali, Grossi and Neves (2013) proved existence for the discrete sequence $\\alpha_k=2(k-1)$, $k\\in\\mathbb N$, and conjectured that non-radial solutions may exist only at these special values. We disprove this conjecture by establishing existence for a continuum of exponents near each \\(\\alpha_k\\)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31670","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/2606.31670/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"}