{"paper":{"title":"On the triharmonic Lane-Emden equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Senping Luo, Wenming Zou","submitted_at":"2016-07-16T08:29:54Z","abstract_excerpt":"We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: \\begin{equation}\\nonumber (-\\Delta)^3 u=|u|^{p-1}u \\hbox{ in } \\mathbb{R}^n, \\end{equation} where $p$ is below the Joseph-Lundgren exponent. As a byproduct we also obtain a new monotonicity formula for the triharmonic maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04719","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":""},"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"}