{"paper":{"title":"Morse index of radial nodal solutions of H\\'enon type equations in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ederson Moreira dos Santos, Filomena Pacella","submitted_at":"2015-03-10T17:32:45Z","abstract_excerpt":"We consider non-autonomous semilinear elliptic equations of the type \\[ -\\Delta u = |x|^{\\alpha} f(u), \\ \\ x \\in \\Omega, \\ \\ u=0 \\quad \\text{on} \\ \\ \\partial \\Omega, \\] where $\\Omega \\subset {\\mathbb R}^2$ is either a ball or an annulus centered at the origin, $\\alpha >0$ and $f: {\\mathbb R}\\ \\rightarrow {\\mathbb R}$ is $C^{1, \\beta}$ on bounded sets of ${\\mathbb R}$. We address the question of estimating the Morse index $m(u)$ of a sign changing radial solution $u$. We prove that $m(u) \\geq 3$ for every $\\alpha>0$ and that $m(u)\\geq \\alpha+ 3$ if $\\alpha$ is even. If $f$ is superlinear the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02999","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"}