{"paper":{"title":"Bubble concentration on spheres for supercritical elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Filomena Pacella","submitted_at":"2013-02-12T12:49:30Z","abstract_excerpt":"We consider the supercritical Lane-Emden problem $$(P_\\eps)\\qquad\n  -\\Delta v= |v|^{p_\\eps-1} v \\ \\hbox{in}\\ \\mathcal{A} ,\\quad u=0\\ \\hbox{on}\\ \\partial\\mathcal{A} $$\n  where $\\mathcal A$ is an annulus in $\\rr^{2m},$ $m\\ge2$ and $p_\\eps={(m+1)+2\\over(m+1)-2}-\\eps$, $\\eps>0.$\n  We prove the existence of positive and sign changing solutions of $(P_\\eps)$ concentrating and blowing-up, as $\\eps\\to0$, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem $(P_\\eps)$ into a nonhomogeneous p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2773","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"}