Semilinear elliptic equations on manifolds with nonnegative Ricci curvature

  • Giovanni Catino

    Politecnico di Milano, Milano, Italy
  • Dario Daniele Monticelli

    Politecnico di Milano, Milano, Italy
Semilinear elliptic equations on manifolds with nonnegative Ricci curvature cover

A subscription is required to access this article.

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.

Cite this article

Giovanni Catino, Dario Daniele Monticelli, Semilinear elliptic equations on manifolds with nonnegative Ricci curvature. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1484