Gradient estimates for a class of quasilinear elliptic equations on manifolds

In this paper, we mainly investigate some local and global properties of positive solutions to the degenerate elliptic equation Δp u + a∇ u^p + b u^q <roman>e</roman>^c u= 0 defined on a Riemannian manifold. We establish Cheng-Yau type gradient estimates for positive solutions of this equation. As corollaries, we derive Harnack inequalities and Liouville theorems for such solutions.