  The dynamical and stationary behaviors of a fourth-order equation in the unit
ball with clamped boundary conditions and a singular reaction term are
investigated. The equation arises in the modeling of microelectromechanical
systems (MEMS) and includes a positive voltage parameter $\lambda$. It is shown
that there is a threshold value $\lambda_*>0$ of the voltage parameter such
that no radially symmetric stationary solution exists for $\lambda>\lambda_*$,
while at least two such solutions exist for $\lambda\in (0,\lambda_*)$. Local
and global well-posedness results are obtained for the corresponding hyperbolic
and parabolic evolution problems as well as the occurrence of finite time
singularities when $\lambda>\lambda_*$.
