{"paper":{"title":"On semilinear elliptic equations with diffuse measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrzej Rozkosz, Tomasz Klimsiak","submitted_at":"2018-01-02T12:52:29Z","abstract_excerpt":"We consider semilinear equation of the form $-Lu=f(x,u)+\\mu$, where $L$ is the operator corresponding to a transient symmetric regular Dirichlet form ${\\mathcal E}$, $\\mu$ is a diffuse measure with respect to the capacity associated with ${\\mathcal E}$, and the lower-order perturbing term $f(x,u)$ satisfies the sign condition in $u$ and some weak integrability condition (no growth condition on $f(x,u)$ as a function of $u$ is imposed). We prove the existence of a solution under mild additional assumptions on ${\\mathcal E}$. We also show that the solution is unique if $f$ is nonincreasing in $u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00633","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"}