{"paper":{"title":"Shooting Method with Sign-Changing Nonlinearity","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Congming Li, Ze Cheng","submitted_at":"2014-07-26T11:05:26Z","abstract_excerpt":"In this paper, we study the existence of solution to a nonlinear system: \\begin{align}\n  \\left\\{\\begin{array}{cl}\n  -\\Delta u_{i} = f_{i}(u) & \\text{in } \\mathbb{R}^n,\n  u_{i} > 0 & \\text{in } \\mathbb{R}^n, \\, i = 1, 2,\\cdots, L\n  % u_{i}(x) \\rightarrow 0 & \\text{uniformly as } |x| \\rightarrow \\infty\n  \\end{array}\n  \\right. \\end{align} for sign changing nonlinearities $f_i$'s. Recently, a degree theory approach to shooting method for this broad class of problems is introduced in \\cite{LiarXiv13} for nonnegative $f_i$'s. However, many systems of nonlinear Sch\\\"odinger type involve interaction w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7121","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"}