{"paper":{"title":"On positive solutions of fully nonlinear degenerate Lane-Emden type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Galise","submitted_at":"2018-01-20T11:09:32Z","abstract_excerpt":"We prove existence and uniqueness results of positive viscosity solutions of fully nonlinear degenerate elliptic equations with power-like zero order perturbations in bounded domains. The principal part of such equations is either $\\mathcal{P}^-_{k}(D^2u)$ or $\\mathcal{P}^+_{k}(D^2u)$, some sort of \\lq\\lq truncated Laplacians\\rq\\rq, given respectively by the smallest and the largest partial sum of $k$ eigenvalues of the Hessian matrix. New phenomena with respect to the semilinear case occur. Moreover, for $\\mathcal{P}^-_{k}$, we explicitely find the critical exponent $p$ of the power nonlinear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06659","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"}