Inserted: 19 oct 2017
Last Updated: 11 jan 2018
Journal: Advances in Nonlinear Analysis
We present a geometric formula of Poincar\'e type, which is inspired by a classical work of Sternberg and Zumbrun, and we provide a classification result of stable solutions of linear elliptic problems with nonlinear Robin conditions on Riemannian manifolds with nonnegative Ricci curvature.
The result obtained here is a refinement of a result recently established by Bandle, Mastrolia, Monticelli and Punzo.