Inequalities for Lower-Order Eigenvalues of a Fourth-Order Elliptic Operator

In this paper, we investigate the Dirichlet weighted eigenvalues problem of a fourth-order elliptic operator with variable coefficients on a bounded domain with smooth boundary in $\mathbb{R}^n$. We establish some inequalities for lower-order eigenvalues of this problem. In particular, our results contain an inequality for eigenvalues of the biharmonic operator derived by Cheng, Huang, and Wei.