  In this paper we investigate gradient Yamabe solitons, either steady or
shrinking, that can be isometrically immersed into space forms as hypersurfaces
that admit an upper bound on the norm of their second fundamental form. Those
solitons satisfying an additional condition, that could be constant mean
curvature or the number of critical points of the potential function being at
most one, are fully classified. Our argument is based on the weak Omori-Yau
principle for the drifted Laplacian on Riemannian manifolds.
