{"paper":{"title":"Quasilinear and Hessian type equations with exponential reaction and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Veron (LMPT), Quoc-Hung Nguyen (LMPT)","submitted_at":"2013-05-19T06:57:23Z","abstract_excerpt":"We prove existence results concerning equations of the type $-\\Delta_pu=P(u)+\\mu$ for $p>1$ and $F_k[-u]=P(u)+\\mu$ with $1\\leq k<\\frac{N}{2}$ in a bounded domain $\\Omega$ or the whole $\\mathbb{R}^N$, where $\\mu$ is a positive Radon measure and $P(u)\\sim e^{au^\\beta}$ with $a>0$ and $\\beta\\geq 1$. Sufficient conditions for existence are expressed in terms of the fractional maximal potential of $\\mu$. Two-sided estimates on the solutions are obtained in terms of some precise Wolff potentials of $\\mu$. Necessary conditions are obtained in terms of Orlicz capacities. We also establish existence re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4332","kind":"arxiv","version":6},"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"}