{"paper":{"title":"Remarks on nonlinear equations with measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Moshe Marcus","submitted_at":"2011-02-28T15:44:42Z","abstract_excerpt":"We study the Dirichlet boundary value problem for equations with absorption of the form $-\\Delta u+g\\circ u=\\mu$ in a bounded domain $\\Omega\\subset R^N$ where $g$ is a continuous odd monotone increasing function. Under some additional assumptions on $g$, we present necessary and sufficient conditions for existence when $\\mu$ is a finite measure. We also discuss the notion of solution when the measure $\\mu$ is positive and blows up on a compact subset of $\\Gw$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5692","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"}