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Abstract <p> We consider a spectral problem for a fourth-order differential operator on the unit intervalwith two boundary conditions containing the spectral parameter. We assume that the coefficientof the differential expression is an absolutely continuous function. The main result is a sharpeigenvalue asymptotics at high energy. This asymptotics shows a nonstandard high-energy effectcaused by the presence of the spectral parameter in the boundary conditions.</p>

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Asymptotics of the Spectrum for a Fourth-Order Differential Operator with a Spectral Parameter in Two Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • D. M. Polyakov

摘要

Abstract

We consider a spectral problem for a fourth-order differential operator on the unit intervalwith two boundary conditions containing the spectral parameter. We assume that the coefficientof the differential expression is an absolutely continuous function. The main result is a sharpeigenvalue asymptotics at high energy. This asymptotics shows a nonstandard high-energy effectcaused by the presence of the spectral parameter in the boundary conditions.