{"paper":{"title":"Existence of a solution to a nonlinear equation","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.G.Ramm","submitted_at":"2004-10-20T21:19:14Z","abstract_excerpt":"Equation $(-\\Delta+k^2)u+f(u)=0$ in $D$, $u\\mid_{\\partial D}=0$, where $k=\\const>0$ and $D\\subset\\R^3$ is a bounded domain, has a solution if $f:\\R\\to\\R$ is a continuous function in the region $|u|\\geq a$, piecewise-continuous in the region $|u|\\leq a$, with finitely many discontinuity points $u_j$ such that $f(u_j\\pm 0)$ exist, and\n $uf(y)\\geq 0$ for $|u|\\geq a$, where $a\\geq 0$ is an arbitrary fixed number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410452","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"}