On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order

Abstract

The estimate of the upper bounds of eigenvalues for a class of systems of ordinary differential equations with higher order is considered by using the calculus theory. Several results about the upper bound inequalities of the ($n+1$)th eigenvalue are obtained by the first $n$ eigenvalues. The estimate coefficients do not have any relation to the geometric measure of the domain. This kind of problem is interesting and significant both in theory of systems of differential equations and in applications to mechanics and physics.