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have been used to model the dynamics of thin films of viscous fluids, where u(x, t) is the height of the air (liquid) interface. The zero set ∑ u = {u = 0} is the liquid (solid) interface and is sometimes called set of ruptures, which plays a very important role in the study of thin films. The coefficient f(u) reflects surface tension effects, a typical choice is f(u) = u. And the coefficient g(u) of the second-order term reflects additional forces such as gravity g(u) = u, and Van der Waals interactions g(u) = u,m < 0. For more information on the background of the equation (1.2), we refer to [2, 3, 19, 20] and the references therein. If we choose f(u) = u, g(u) = u, where l,m ∈ R, and we consider the steady state of (1.2), we see that if u satisfies the following equation

Nonexistence of Positive Finite Morse Index Solutions to an Elliptic Problem with Singular Nonlinearity