  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.
