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Abstract <p>In this paper, a nonlocal spectral problem for the biharmonic equations in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8164_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> <!--LobJMat2460526Arzikulov-m1--> </InlineEquation>-dimensional ball is studied. It is proven that the problem has a complete system of eigenfunctions and associated functions in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8164_Article_IEq2.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{\frac{3}{2}}(\Omega)\)</EquationSource> <!--LobJMat2460526Arzikulov-m2--> </InlineEquation>, and the eigenvalues asymptotically approach the real axis.</p>

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On the Eigenfunctions and Associated Functions of a Nonlocal Spectral Problem for a Biharmonic Equation

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • A. U. Arzikulov

摘要

Abstract

In this paper, a nonlocal spectral problem for the biharmonic equations in \(n\) -dimensional ball is studied. It is proven that the problem has a complete system of eigenfunctions and associated functions in \(H^{\frac{3}{2}}(\Omega)\) , and the eigenvalues asymptotically approach the real axis.