We study the electrostatic MEMS-device equation, ut − ∆u = λ|x| β (1−u)p , with Dirichlet boundary condition. First, we describe the touchdown of non-stationary solution in accordance with the total set of stationary solutions. Then, we classify radially symmetric stationary solutions and their radial Morse indices. Finally, we show the Morse-Smale property for radially symmetric non-stationary solutions.