{"paper":{"title":"Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hoang-Hung Vo, Phuoc-Tai Nguyen","submitted_at":"2014-07-25T15:13:11Z","abstract_excerpt":"We study the following quasilinear elliptic equation $$ -\\Delta_p u + (\\beta\\Phi(x)-a(x)) u^{p-1} + b(x)g(u)=0 \\quad \\text{in } \\mathbb{R}^N \\quad \\quad \\quad (P_\\beta) $$ where $p>1$, $\\Phi \\in L^\\infty_{loc}(\\mathbb{R}^N)$, $a,b \\in L^\\infty(\\mathbb{R}^N)$, $\\beta,b,g \\geq 0$. We provide a sharp criterion in terms of generalized principal eigenvalue for existence/nonexistence of positive solutions of ($P_\\beta$) in suitable classes of functions. We derive the uniqueness result of ($P_\\beta$) in those classes. Under additional conditions on $\\Phi$, we further show that :\n  i) either for every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6931","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"}