{"paper":{"title":"Global bifurcation for asymptotically linear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Genoud","submitted_at":"2011-06-29T08:58:17Z","abstract_excerpt":"We prove global asymptotic bifurcation for a very general class of asymptotically linear Schr\\\"odinger equations \\begin{equation}\\label{1} \\{{array}{lr} \\D u + f(x,u)u = \\lam u \\quad \\text{in} \\ {\\mathbb R}^N, u \\in H^1({\\mathbb R}^N)\\setmimus\\{0\\}, \\quad N \\ge 1. {array}. \\end{equation} The method is topological, based on recent developments of degree theory. We use the inversion $u\\to v:= u/\\Vert u\\Vert_X^2$ in an appropriate Sobolev space $X=W^{2,p}({\\mathbb R}^N)$, and we first obtain bifurcation from the line of trivial solutions for an auxiliary problem in the variables $(\\lambda,v) \\in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5879","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"}