{"paper":{"title":"Weak solutions of semilinear elliptic equation involving Dirac mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen, Jianfu Yang, Patricio Felmer","submitted_at":"2015-09-19T01:31:48Z","abstract_excerpt":"In this paper, we study the following elliptic problem with Dirac mass \\begin{equation}\\label{eq 0.1}\n  -\\Delta u=Vu^p+k \\delta_0\\quad\n  {\\rm in}\\quad \\mathbb{R}^N, \\qquad \\lim_{|x|\\to+\\infty}u(x)=0,\n  \\end{equation} where $N>2$, $p>0$, $k>0$, $\\delta_0$ is Dirac mass at the origin, the function $V$ is a locally Lipchitz continuous in $\\mathbb{R}^N\\setminus\\{0\\}$ satisfying $$ V(x)\\le \\frac{c_1}{|x|^{a_0}(1+|x|^{a_\\infty-a_0})} $$ with $a_0<N,\\ a_\\infty>a_0 $ and $c_1>0$. We obtain two positive solutions of (\\ref{eq 0.1}) with additional conditions for parameters on $a_\\infty, a_0$, $p$ and $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05839","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"}