Essential Self-adjointness of Differential Operators on Riemannian Manifolds

In this paper we have studied the essential self-adjointness for the differential operator of the form: T=Δ⁸+V, on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential V satisfying a bound from below by a non-positive function depending on the distance from a point. We give sufficient condition for the essential self-adjointness of such differential operator on Riemannian Manifolds.