{"paper":{"title":"Solutions with large number of peaks for a slightly supercritical nonlinear equation in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yixing Pu","submitted_at":"2025-06-02T13:25:36Z","abstract_excerpt":"We investigate the existence of solutions to the semilinear equation with a slightly supercritical exponent in dimension three,\n  \\begin{align*}\n  -\\Delta u=K(x) u^{5+\\mu},\\quad u>0 ~\\text{in}~ \\mathbf{B}, \\quad u=0 ~\\text{on}~ \\partial \\mathbf{B},\n  \\end{align*}\n  where $\\mu >0$, $\\mathbf{B}$ is the unit ball in $\\mathbb{R}^3$, $K(x)$ is a nonnegative radial function under suitable condition on $K$. We prove the existence of positive multi-peak solutions for $\\mu>0$ small enough. All peaks of our solutions approach the boundary $\\partial\\mathbf{B}$ as $\\mu\\rightarrow 0$. Moreover, the number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01652","kind":"arxiv","version":2},"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/2506.01652/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"}