The paper first study the steady-state thin film type equation ∇ ⋅ ( u n | ∇ Δ u | q − 2 ∇ Δ u ) − δ u m Δ u = f ( x , u ) with Navier boundary conditions in multidimensional space. By the truncation method, a fixed point argument and some energy estimates, the existence and asymptotic limit δ → 0 for the positive weak solutions are given. Second, the parabolic equation u t + ( u n | u x x x | q − 2 u x x x ) x − δ u m u x x = 0 with a Navier boundary in one-dimensional space is researched. The existence is obtained by applying a semi-discrete method for the time variable and solving the corresponding elliptic problem. The uniqueness is shown for q = 2 depending on an energy estimate. In addition, the iteration relation of the semi-discrete problem gives an exponential decay result for the time t → ∞ . The thin film equation, which is usually used to describe the motion of a very thin layer of viscous in compressible fluids along an inclined plane, is a class of nonlinear fourth-order parabolic equations and the maximum principle does not hold directly. For applying the classic theory of partial differential equation, the paper transforms the fourth-order problem into a second-order elliptic–elliptic system or a second-order parabolic–elliptic system.