{"paper":{"title":"Stable solutions and finite Morse index solutions of nonlinear elliptic equations with Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wonjeong Jeong, Youngae Lee","submitted_at":"2013-03-21T03:06:45Z","abstract_excerpt":"We are concerned with Liouville-type results of stable solutions and finite Morse index solutions for the following nonlinear elliptic equation with Hardy potential: \\begin{displaymath} \\Delta u+\\dfrac{\\mu}{|x|^2}u+|x|^l |u|^{p-1}u=0 \\qquad \\textrm{in}\\ \\ \\Omega, \\end{displaymath} where $\\Omega=\\RN$, $\\RN\\setminus\\{0\\}$ for $N\\geq3$, $p>1$, $l>-2$ and $\\mu<(N-2)^2/4$. Our results depend crucially on a new critical exponent $p=p_c(l,\\mu)$ and the parameter $\\mu$ in Hardy term. We prove that there exist no nontrivial stable solution and finite Morse index solution for $1<p<p_c(l,\\mu)$. We also o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5149","kind":"arxiv","version":2},"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"}