{"paper":{"title":"On the generalized principal eigenvalue of quasilinear operators","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":"2017-05-25T14:44:20Z","abstract_excerpt":"The notions of generalized principal eigenvalue for linear second order elliptic operators in general domains introduced by Berestycki et al. \\cite{BNV,BR0,BR3} have become a very useful and important tool in analysis of partial differential equations. In this paper, we extend these notions for quasilinear operator of the form $$\\CK_V[u]:=-\\Delta_p u +Vu^{p-1},\\quad\\quad u \\geq0.$$ This operator is a natural generalization of self-adjoint linear operators. If $\\O$ is a smooth bounded domain, we already proved in \\cite{NV} that the generalized principal eigenvalue coincides with the (classical)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09204","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"}