{"paper":{"title":"On the solutions of a singular elliptic equation concentrating on a circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B.B.Manna, P.N.Srikanth","submitted_at":"2013-10-22T08:21:42Z","abstract_excerpt":"Let $A=\\{x\\in \\R^{2N+2} : 0< a< |x| <b\\}$ be an annulus. Consider the following singularly perturbed elliptic problem on $A$\n  \\begin{equation}\n  \\begin{array}{lll}\n  -\\eps^2{\\De u} + |x|^{\\alpha}u = |x|^{\\alpha}u^p, &\\mbox{\\qquad in} A \\notag u>0 &\\mbox{\\qquad in} A\n  \\frac{\\partial u}{\\partial\\nu} = 0 &\\mbox{\\qquad on} \\partial A\n  \\end{array} %\\label{a1}\n  \\end{equation} $1<p<2^*-1$. We shall show that there exists a positive solution $u_\\eps$ concentrating on an $S^1$ orbit as $\\eps\\to 0$. We prove this by reducing the problem to a lower dimensional one and analyzing a single point concent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5831","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"}