{"paper":{"title":"Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and Hardy-Sobolev exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mousomi Bhakta","submitted_at":"2014-10-29T05:43:44Z","abstract_excerpt":"We study the existence and multiplicity of sign changing solutions of the following equation $ \\begin{cases} -\\Delta u = \\mu |u|^{2^{\\star}-2}u+\\frac{|u|^{2^{*}(t)-2}u}{|x|^t}+a(x)u \\quad\\text{in}\\quad \\Omega, u=0 \\quad\\text{on}\\quad\\partial\\Omega, \\end{cases} $where $\\Omega$ is a bounded domain in $R^N$, $0\\in\\partial\\Omega$, all the principal curvatures of $\\partial\\Omega$ at $0$ are negative and $\\mu\\geq 0, \\ \\ a>0, \\ \\ N\\geq 7, \\ \\ 0<t<2, \\ \\ 2^{\\star}=\\frac{2N}{N-2}$ and $2^{\\star}(t)=\\frac{2(N-t)}{N-2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7880","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"}