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

被引：3

作者：

Braeutigam, I. N. ^{[1
]}

Polyakov, D. M. ^{[2
]}

机构：

[1] Northern Arctic Fed Univ, Arkhangelsk 163002, Russia

[2] Russian Acad Sci, Vladikavkaz Sci Ctr, Southern Math Inst, Vladikavkaz 362027, Russia

来源：

DIFFERENTIAL EQUATIONS | 2018年 / 54卷 / 04期

关键词：

STURM-LIOUVILLE OPERATORS; SPECTRAL-ANALYSIS; ADJOINT;

D O I：

10.1134/S0012266118040031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：450 / 467

页数：18

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