  This article presents new local and global gradient estimates of Li-Yau type
for positive solutions to a class of nonlinear elliptic equations on smooth
metric measure spaces involving the Witten Laplacian. The estimates are derived
under natural lower bounds on the associated Bakry-\'Emery Ricci curvature
tensor and find utility in proving general Harnack inequalities and
Liouville-type theorems to mention a few. The results here unify, extend and
improve various existing results in the literature for special nonlinearities
already of huge interest and applications. Some important consequences are
presented and discussed.
