Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds

We prove some inequalities of Payne-P\'olya-Weinberger-Yang type for eigenvalues fourth-order elliptic operators in weighted divergence form on complete Riemannian manifolds which generalizes the corresponding result clamped plate problem. also estimates lower order that contain from literature. As an application our results, we obtain bi-drifted Cheng-Yau operator.