{"paper":{"title":"Multiple nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sergio Rolando","submitted_at":"2017-08-03T17:20:40Z","abstract_excerpt":"Many existence and nonexistence results are known for nonnegative radial solutions $u\\in D^{1,2}(\\mathbb{R}^{N})\\cap L^{2}(\\mathbb{R}^{N},\\left|x\\right| ^{-\\alpha }dx)$ to the equation \\[ -\\triangle u+\\dfrac{A}{\\left| x\\right| ^{\\alpha }}u=f\\left( u\\right) \\quad \\textrm{in }\\mathbb{R}^{N},\\quad N\\geq 3,\\quad A,\\alpha >0, \\] with nonlinearites satisfying $\\left| f\\left( u\\right) \\right| \\leq \\left(\\mathrm{const.}\\right) u^{p-1}$ for some $p>2$. Existence of nonradial solutions, by contrast, is known only for $N\\geq 4$, $\\alpha =2$, $f\\left( u\\right) =u^{(N+2)/(N-2)}$ and $A$ large enough. Here "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01228","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"}