On steady states of van der Waals force driven thin film equations

Let Omega subset of R (N), N >=, 2 be a bounded smooth domain and a > t. We are interested in the singular elliptic equation Delta h =1/alpha h(-alpha)-p in Omega with Neumann boundary conditions. In this paper, a complete description of all continuous radially symmetric solutions is given. In particular, we construct nontrivial smooth solutions as well as rupture solutions. Here a continuous solution is said to be a rupture solution if its zero set is nonempty. When N = 2 and alpha = 3, the equation is used to model steady states of van der Waals force driven thin films of viscous fluids. We also consider the physical problem when total volume of the fluid is prescribed.