{"paper":{"title":"Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Luciano Mari, Marco Magliaro, Marco Rigoli, Paolo Mastrolia","submitted_at":"2010-03-30T10:17:11Z","abstract_excerpt":"The aim of this paper is to study the qualitative behaviour of non-negative entire solutions of certain differential inequalities involving gradient terms on the Heisenberg group. We focus our investigation on the two classes of inequalities of the form $\\Delta^\\phi u \\ge f(u)l(|\\nabla u|)$ and $\\Delta^\\phi u \\ge f(u) - h(u) g(|\\nabla u|)$, where $f,l,h,g$ are non-negative continuous functions  satisfying certain monotonicity properties. The operator  $\\Delta^\\phi$, called the $\\phi$-Laplacian, can be viewed as a natural generalization of the $p$-Laplace operator recently considered by various"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5780","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"}