ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF FOURTH-ORDER DIFFERENTIAL OPERATORS WITH SPECTRAL PARAMETER IN THE BOUNDARY CONDITIONS

被引：0
|
作者：
Polyakov, Dmitry M. [1 ]
机构：
[1] RAS, Southern Math Inst, Vladikavkaz Sci Ctr, 53 Vatutin str, Vladikavkaz 362025, Russia
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 2024卷 / 62期
关键词：
Eigenvalue; asymptotic behavior; fourth-order eigenvalue problem; spectral parameter in boundary conditions; fourth-order differential operator; EIGENFUNCTION-EXPANSIONS; CONVERGENCE;
D O I：
10.58997/ejde.2024.62
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
. We consider a spectral problem for a fourth-order differential equation with spectral parameter dependent boundary conditions. We determine the high energy eigenvalue behavior for this operator. Moreover, if the coefficient of differential equation is sufficiently smooth, we can obtain sharp eigenvalue asymptotic behavior. This behavior exhibits a non-standard highfrequency effect generated by the spectral parameter in the boundary conditions.
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页码：1 / 30
页数：30
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