{"paper":{"title":"A note on the eigenvalues of fractional Hardy-Sobolev operator with indefinite weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sarika Goyal","submitted_at":"2016-07-26T08:04:37Z","abstract_excerpt":"In this article, we study the eigenvalue of nonlinear $p-$fractional Hardy operator \\begin{align*} (-\\Delta)_p^{\\alpha}u - \\mu \\frac{|u|^{p-2}u}{|x|^{p\\alpha}} = \\lambda V(x) |u|^{p-2}u \\; \\text{in}\\; \\Omega, \\quad u = 0 \\; \\mbox{in}\\; \\mathbb{R}^n \\setminus\\Omega, \\end{align*} where $n>p\\alpha$, $p\\geq2$, $\\alpha\\in(0,1)$, $0\\leq \\mu <C_{n,\\alpha,p}$ and $\\Omega$ is a domain in $\\mathbb{R}^n$ with Lipschitz boundary containing $0$. In particular, $\\Omega=\\mathbb{R}^n$ is admitted. The weight function $V$ may change sign and may have singular points. We also show that the least positive eigenv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07580","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"}