{"paper":{"title":"Entire nodal solutions to the pure critical exponent problem for the $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luis Lopez Rios, M\\'onica Clapp","submitted_at":"2017-11-10T03:58:48Z","abstract_excerpt":"We establish the existence of multiple sign-changing solutions to the quasilinear critical problem $$-\\Delta_{p} u=|u|^{p^*-2}u, \\qquad u\\in D^{1,p}(\\mathbb{R}^{N}),$$ for $N\\geq4$, where $\\Delta_{p}u:=\\mathrm{div}(|\\nabla u|^{p-2}\\nabla u)$ is the $p$-Laplace operator, $1<p<N$ and $p^*:=\\frac{Np}{N-p}$ is the critical Sobolev exponent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03681","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"}