  In this paper, we look for properties of gradient Yamabe solitons on top of
warped product manifolds. Utilizing the maximum principle, we find lower bound
estimates for both the potential function of the soliton and the scalar
curvature of the warped product. By slightly modifying Li-Yau's technique so
that we can handle drifting Laplacians, we were able to find three different
gradient estimates for the warping function, one for each sign of the scalar
curvature of the fiber manifold. As an application, we exhibit a nonexistence
theorem for gradient Yamabe solitons possessing certain metric properties on
the base of the warped product.
