  By the application of the generalized Israel junction conditions we derive
cosmological equations for the fourth-order $f(R)$ brane gravity and study
their cosmological solutions. We show that there exists a non-static solution
which describes a four-dimensional de-Sitter $(dS_4)$ brane embedded in a
five-dimensional anti-de-Sitter $(AdS_5)$ bulk for a vanishing Weyl tensor
contribution. On the other hand, for the case of a non-vanishing Weyl tensor
contribution, there exists a static brane only. We claim that in order to get
some more general non-static $f(R)$ brane configurations, one needs to admit a
dynamical matter energy-momentum tensor in the bulk rather than just a bulk
cosmological constant.
