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In this work the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions we arrive at the following fourth-order differential equation 1 r { r [ 1 r (rφ′) ′ ]′}′ = 1 r φ ′ φ ′′ + λG(r), 0 < r < 1. It is non-self adjoint and it does not have exact solutions and also it admits multiple 1 solutions. Here λ ∈ R measures the intensity of the flux and G is stationary 2 flux. Solution depends on the size of the parameter λ. We use monotone iterative 3 technique and integral equations along with upper and lower solutions to prove 4 that solutions exist. We establish the qualitative properties of the solutions and 5 provide bounds for the values of the parameter λ, which help us to separate the 6 existence from nonexistence. These results complement some existing results in 7 the literature. To verify the analytical results we also propose a new computational 8 iterative technique and use it to verify the bounds on λ and dependence of solutions 9 for these computed bounds on λ. 10

Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth