Spectral Estimates for the Fourth-Order Operator with Matrix Coefficients

Abstract

The fourth-order differential operator with matrix coefficients with the domain determined by quasi-periodic boundary conditions is considered. For this operator, the asymptotics of the arithmetic mean of the eigenvalues is found. Moreover, for various special cases, the asymptotics of the eigenvalues is also obtained. The spectral characteristics in the case of periodic and antiperiodic boundary conditions are studied separately. The results are better than those known before.