On the non-existence of positive solutions to a class of quasilinear elliptic equations on complete Riemannian manifolds

Jie He, Youde Wang

Published 2023-11-22Version 1

This paper uses Nash-Moser iteration method to study solutions to the nonlinear elliptic equation $\Delta_pv+b|\nabla v|^q+cv^r =0$ on a complete Riemannian manifold $(M,g)$, where $b, c, p, q$ and $r$ are constants. When $b$ and $c$ have the same sign, we give some regions of $(q, r)$ where the Cheng-Yau type gradient estimate holds. By generalizing some results of \cite{MR1879326} to manifold, we obtain a more wider range of $(q,r)$ for Liouville properties.