On the Asymptotics of Eigenvalues of a Fourth-Order Differential Operator with Matrix Coefficients

We study a fourth-order differential operator with matrix coefficients whose domain is determined by the Dirichlet boundary conditions. An asymptotics of the weighted average of the eigenvalues of this operator is obtained in the general case. As a consequence of this result, we present the asymptotics of the eigenvalues in several special cases. The obtained results significantly improve the already known asymptotic formulas for the eigenvalues of a one-dimensional fourth-order differential operator.