{"paper":{"title":"Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sofya Lyakhova, Vitali Liskevich, Vitaly Moroz","submitted_at":"2006-04-21T17:57:08Z","abstract_excerpt":"We study the existence and nonexistence of positive (super) solutions to the nonlinear $p$-Laplace equation $$-\\Delta_p u-\\frac{\\mu}{|x|^p}u^{p-1}=\\frac{C}{|x|^{\\sigma}}u^q$$ in exterior domains of ${\\R}^N$ ($N\\ge 2$). Here $p\\in(1,+\\infty)$ and $\\mu\\le C_H$, where $C_H$ is the critical Hardy constant. We provide a sharp characterization of the set of $(q,\\sigma)\\in\\R^2$ such that the equation has no positive (super) solutions.\n  The proofs are based on the explicit construction of appropriate barriers and involve the analysis of asymptotic behavior of super-harmonic functions associated to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604469","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"}