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The existence and nonexistence of stationary radial solutions to the ellipticpartial differential equation arising in the molecular beam epitaxy arestudied. The fourth-order radial equation is non-self adjoint and has no exactsolutions. Also, it admits multiple solutions. Furthermore, solutions depend onthe size of the parameter. We show that solutions exist for small positivevalues of this parameter. For large positive values of this parameter, we provethe nonexistence of solutions. We establish the qualitative properties of thesolutions and provide bounds for the values of this parameter, which help us toseparate the existence from nonexistence. We propose a new numerical scheme tocapture the radial solutions. The results show that the iterative method is ofbetter accuracy, more convenient and efficient for solving BVPs, which havemultiple solutions. We verify theoretical results by numerical results. We alsosee the existence of solutions for negative values of the same parameter.

Existence and nonexistence results of radial solutions to singular BVPs arising in epitaxial growth theory