Existence and nonexistence results of radial solutions to singular BVPs arising in epitaxial growth theory (1911.04979v1)

Abstract: The existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. The fourth-order radial equation is non-self adjoint and has no exact solutions. Also, it admits multiple solutions. Furthermore, solutions depend on the size of the parameter. We show that solutions exist for small positive values of this parameter. For large positive values of this parameter, we prove the nonexistence of solutions. We establish the qualitative properties of the solutions and provide bounds for the values of this parameter, which help us to separate the existence from nonexistence. We propose a new numerical scheme to capture the radial solutions. The results show that the iterative method is of better accuracy, more convenient and efficient for solving BVPs, which have multiple solutions. We verify theoretical results by numerical results. We also see the existence of solutions for negative values of the same parameter.