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<p>The purpose of this paper is to study the Sturm–Liouville problem with boundary condition dependent rationally on the eigenparameter. By defining the weak solutions, constructing a suitable Hilbert space, and introducing certain compact operators in the new Hilbert space, we reduce the problem under consideration to an operator pencil. Then, we show that the weak eigenfunctions for this kind of problem form a Riesz basis of the Hilbert space. Furthermore, we obtain the asymptotic behavior of the eigenvalues.</p>

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Weak eigenfunctions of Sturm–Liouville problem with boundary condition dependent rationally on the eigenparameter

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Zhiyu Li,
  • Zhaowen Zheng,
  • Kun Li,
  • Jianfang Qin

摘要

The purpose of this paper is to study the Sturm–Liouville problem with boundary condition dependent rationally on the eigenparameter. By defining the weak solutions, constructing a suitable Hilbert space, and introducing certain compact operators in the new Hilbert space, we reduce the problem under consideration to an operator pencil. Then, we show that the weak eigenfunctions for this kind of problem form a Riesz basis of the Hilbert space. Furthermore, we obtain the asymptotic behavior of the eigenvalues.