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Mathematics > Analysis of PDEs

arXiv:2203.03345 (math)
[Submitted on 7 Mar 2022 (v1), last revised 18 Mar 2022 (this version, v2)]

Title:Semilinear elliptic equations on manifolds with nonnegative Ricci curvature

Authors:Giovanni Catino, Dario Daniele Monticelli
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Abstract:In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature. We show in the subcritical case that all nonnegative solutions vanish identically. Moreover, under some natural assumptions, in the critical case we prove a strong rigidity result, namely we classify all nontrivial solutions showing that they exist only if the potential is constant and the manifold is isometric to the Euclidean space.
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
Cite as: arXiv:2203.03345 [math.AP]
  (or arXiv:2203.03345v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2203.03345

Submission history

From: Giovanni Catino [view email]
[v1] Mon, 7 Mar 2022 12:43:53 UTC (18 KB)
[v2] Fri, 18 Mar 2022 07:35:15 UTC (18 KB)
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