{"paper":{"title":"A supercritical scalar field equation with a forcing term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Shinya Okabe, Tokushi Sato","submitted_at":"2019-02-05T09:37:06Z","abstract_excerpt":"This paper is concerned with the elliptic problem for a scalar field equation with a forcing term \\begin{equation} \\tag{P}-\\Delta u+u=u^p+ \\kappa \\mu \\quad \\mbox{in} \\quad{\\bf R}^N, \\quad u>0 \\quad \\mbox{in} \\quad {\\bf R}^N, \\quad u(x)\\to 0\\quad \\mbox{as} \\quad |x| \\to \\infty, \\end{equation} where $N\\ge 2$, $p>1$, $\\kappa>0$ and $\\mu$ is a Radon measure in ${\\bf R}^N$ with a compact support. Under a suitable integrability condition on $\\mu$, we give a complete classification of the solvability of problem~(P) with $1<p<p_{JL}$. Here $p_{JL}$ is the Joseph-Lundgren exponent defined by $$\n  p_{JL"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01606","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"}