Positive solutions of the $p$-Laplacian with potential terms on weighted Riemannian manifolds with linear diameter growth

Abstract

In this paper, we consider the $p$-Laplacian with potential terms on a connected, noncompact, complete weighted Riemannian manifold whose Ricci curvature has quadratic decay, or a lower bound. We investigate the structure and the behavior of positive solutions under the assumption that the metric spheres of the Riemannian manifold have linear diameter growth.