Let Ω ⊂ R N , N ≥ 2 be a bounded smooth domain and α > 1. We are interested in the singular elliptic equation with Neumann boundary conditions. In this paper, we gave a complete description of all continuous radially symmetric solutions. In particular, we constructed 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 α = 3, the equation has been used to model steady states of van der

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... als force driven thin films of viscous fluids. We also considered the physical problem when total volume of the fluid is prescribed.