  In this paper, under suitable settings, we can obtain the existence of
solutions to a class of prescribed Weingarten curvature equations in warped
product manifolds of special type by the standard degree theory based on the a
priori estimates for the solutions. This is to say that the existence of closed
hypersurface (which is graphic with respect to the base manifold and whose
$k$-th Weingarten curvature satisfies some constraint) in a given warped
product manifold of special type can be assured.
