Calculus of Variations and Geometric Measure Theory

G. Catino - D. D. Monticelli

Semilinear elliptic equations on manifolds with nonnegative Ricci curvature

created by catino on 07 Mar 2022
modified on 18 Mar 2022

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Submitted Paper

Inserted: 7 mar 2022
Last Updated: 18 mar 2022

Year: 2022

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.


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